What can't you do with Moodle?
There is an Attendance plug-in that can track classroom attendance, there is a Face-to-Face plugin that allows people to sign up and teachers to take attendance. I use F2F. It has some quirks but generally works well. There are several options for course payment stuff (I don't do that). Custom Certificate can be issued when specific tasks are complete and it saves a copy if you want one. Cohorts could be used to assign people to a group of courses for specific qualifications. You could probably issue a certificate from a hidden spot in the site main page when specific courses are complete (I've never tried it but I bet you could figure it out...)
There is Configurable reports or Adhoc reports where you could create reports that pull a student's full course record or compile data.
When people ask me "Can Moodle do..." My response is "Of course. It might not do it the way you envision it, but it can do just about anything." A better question is "What can't Moodle do?" I don't have an answer for that one.