Lots of questions, and these are my ideas and opinions, but please bear in mind, Moodle is Open Source. This means that anything you need that can be considered "enterprise specific", your organization can develop for themselves iff they chose to. Look at it this way, Moodle can be a shell you manipulate for your own purposes, in anyway you need it to. Any development your organization needs it can create itself, without prejudice, it can onsell any such development, it can give it away, it can dump it altogether. You can download and install a copy of Moodle, then develop it anyway you like and build your own updates. What you cannot do is rebadge and sell Moodle. There are other restrictions, of course, but these are all outlined in the EULA and under the GNU Open Source License as well as US Patent laws. In short, you can do almost anything you want to Moodle without waiting for some vague "development team" to produce a patch that may or may not work with the hundred other patches you have already installed.
Can a certificate of completion be automatically generated upon completion of a course, including employee (student) name and date/time of completion?
Yes, certificate module does that.
Can a course be configured to save progress and indicate where an individual should resume work between logins?
Yes - depending on how you want to configure the course, you can start/stop anywhere if you want to recognize prior learning, or grant equivalency.
Can a teacher/admin restrict the order in which activities/topics are taken without the use of conditional grading?
Yes, but you may still need conditional activities, alternatively, you can physically set a course structure up to display a single topic at a time if you really want to maintain a lockstep approach, and you can make your assessment process/system anything you want - within limits of course.
Is there capability to search for course codes? If so, and the code searched for does not exist, can Moodle be configured to generate an online "survey" with form/data collection for requested information to be sent to a chosen destination?
Dunno... never tried it but each course is written and developed in whatever manner you want them to be, and can be searched for inside Moodle, but if you properly structure your menu approach with a mixture of visual and textual clues, there should be an absolute minimum need for searching - it should be thematically or topically intuitive. And, IMNSHO, if an LMS is offering such a search capacity as a major selling point, I would suggest their menu structure might be more than a little suspect.
Can a session of a course be deleted without deleting the entire course? Can courses be deleted?
Yes and no... but this question is a little vague, a course can be deleted, but only by someone with the appropriate permissions, but why delete a course? It can be archived, it can be made part of a complete backup/archive, it can be hidden from user view, but still available to the person(s) who is/are assigned as teacher(s), as site administrator(s),
Can admins enter fields for contract amount/cost data and still be able to mark "no charge" on an individual level to generate calculated fields for breakeven? What about total contract cost (number of chargeable slots filled compared to contract cost/individual charge as breakeven point)?
mmmmm not sure what you are getting at here... but I am not that mercenary with charging. I cannot remember hearing any comments that deny this possibility, if I understand you correctly. AFAIK, you can make whatever rules you want around charging, but that would be between you and whomever you contract with.
Are teacher and admin roles able to toggle fields to view employees (students) by alpha, date enrolled, etc.?
Yes - to a point but why? Who benefits? This is enterprise specific.
Is there a way to put in specific trigger dates per session and/or course for email updates to a chosen destination? Can this be auto-generated?
Yes, you can have commencement and conclusion dates preset, and the course is only available for that period of time, see above about restriuctions on specifying sessions or lessons or topics or weeks.
Is there a report/view that can be used to quickly see for any session or multiple sessions of the same course: #fully approved, #pending (supr), #pending (funds), #chargeable?
Dunno, but of there isn't then any clever PHP/MySQL (or Postgres or Oracle or MSSQL) coder can easily create the necessary reports you need. Again, enterprise specific needs can be met internally.
Can data collection be managed to create accurate course rosters with general enrollment info (name from Active Directory, contacts, unit, supervisor, etc.) and check for dupes?
I understand that is still in development, but how far do you want to go? Again, whatever reports are lacking, see the previous answer.
Can employees (students) request accommodation at time of enrollment? Can this request be automatically forwarded to the teacher?
??? What? Moodle is an LMS and this is way beyond the scope of anything that Moodle has ever offered, but again, if you have a clever PHP developer, or team, you can actually create your own modules to do whatever you want them to do.
Can Cisco Meeting Place/Vidyo recorded sessions be tied to the system for tracking and/or archival purposes?
Dunno, never considered it, but I expect so, there might need to be some tweaking of the recorders, but I cannot think of any reasons why screen grabbers like these can't record things. That seems to me to be something of a system of perfection, a want rather than a need, and such ambition can bring any project unstuck. The individual nature of Moodle though would make this a rather duanting task if you want to record every session of every student.
Can the courses be set up to send an email to supervisor when employee (student) registers?
Of course. But this is always a topic of discussion, and contention. Self enrollment has some uses, but your security around recognition and acceptance is going to need to be pretty tight. As I am in the public education sector, such things are for me, somewhat vague, someone else may be better qualified to answer these questions.
Can an employee be assigned a course which they have to enroll for themselves? Can their status (unassigned, assigned, enrolled, completed) be tracked and viewed in a report? mmmm again, dunno... never bothered with it, but this seems to me to be something of a want than a need. However, having said that, you can develop your own modules for these purposes.
Can admins/teachers customize emails and send them out to entire classes? Do these roles have the option of sending emails to individuals/sessions/courses?
Yes, yes and yes, as long as the SMPT servers are set up correctly and the links between Moodle and the server are right and the email addresses of the recipients are correct, you can even customize the automatic messaging emails.
Is there a way to run reports concerning evaluation data for an individual session, courses overall, averages calculated, etc.? Also, can evaluation data be calculated by instructor/vendor?
Wow! How much tracking and assessing are you doing? Be careful here, you do not want to monster the teaching/instructing staff with this. You can develop grading systems within Moodle, the extent of which can be limited by the tasks set within each course. You can have a fully manual assessment process, a manual/automatic process or fully automatic process, but you will need to be very clear to start with and be constantly vigilant for deviations. Automatic assessments need to be very specific, this is a hardware limitation rather than a programmatic problem, computers have yet to learn how to think and make judgement calls.
Is there a way to print standard lists with the ability to filter results, including but not limited to: training schedule (date range, unit provider, title), training delivered, monthly schedule of classes for a particular location, etc.?
See report comments above, you can manipulate Moodle to do whatever you want here.
Is there a way to produce an ad-hoc report based on key words (e.g., category, title, instructor, dates, etc.)?
Yes, a simplistic preexisting process does exist, but it is somewhat basic, any real sophisitcation is usually enterprise specific, and way outside Moodle.org's vision of a useful product.
Is the data collected in a format that allows for possible future export to PeopleSoftFIN?
What is PeopleSoftFIN? If it uses xml files, then possibly, but this is so enterprise specific, it is really outside the scope of Moodle.
Is the system compatible with older browsers? Most browsers were mentioned in the documents section concerning that topic, so specifically--what about Netscape (yes, I know, who uses Netscape?) and is there a more complete list of supported/unsupported browsers?
AFAIK, there may be specific issues with specific browsers, some older versions of Internet Explorer can break Moodle styles, but this is an IE problem, which has since been fixed in later versions. The ready availability of newer browsers though should render this question moot. I do understand though that even if someone is using Netscape, they are not going to get too much of the modern internet displaying, and as more and more HTML5 is used and IPv6 sites start to dominate, older browsers are going to be relegated to the dustbin. Moodle is not using HTML5 yet, AFAIK, but it will, and when it does then there wuill be compatibility issues.
Moodle is very much a work in progress. It is adaptable to any circumstance you want it to be, almost. You can legally change any part of Moodle you want, you can take control of it and make it your own. The Moodles I run are basic, standard Moodles, the Moodle run by Open University is hugely different. My little Moodles suit the not for profit enterprises they are used in. You do not like something in Moodle, change it to suit your need. AFAIK, none of the other LMS' offer that kind of flexibility.