If I'm reading your question correctly, then no, it's not possible - but it has been asked for in the past. For example, have a look at http://moodle.org/mod/forum/discuss.php?d=3513.
Tim Hunt, one of the Core Developers working on the Quiz module, says that anonymous (Guest) access could be possible - http://moodle.org/mod/forum/discuss.php?d=87819#434842
But for now, it definitely doesn't work as you want. The current documentation explains: "Guest users can never attempt quizzes, even if you give guests the mod/quiz:attempt capability. This is because all information about a user's progress through the quiz must be stored in the database associated with the user doing the attempt, and each user can only have one attempt open at a time. Since all guest users in Moodle share a single user account, letting guests attempt quizzes would just cause a big mess where different guest users' actions would conflict with each other. Therefore, people logged in as guest are never allowed to attempt quizzes."
I was going to point you at the feature request in the Moodle Tracker, so you could vote for it to indicate your desire for this feature. However, as far as I can see, no one has ever been bothered to file this feature request!
I suggest make a Moodle quiz and suggest that they make a email registration (than they can be sure that they get fresh questions and no interference), but provide a set of bogus IDs for those that want anonymity (or are lazy) like:
ID:test1 pw: one
ID:test2 pw: two
ID:test3 pw: three
.... as many as you think might need this simultaneously. Recommend that they don't use an ID that is presently on line and preferentially one that is a higher number than any they see that is in use. (See to it that you have the block showing "currently online" enabled)
I'd better save this before I lose it again.
in the Moodle Tracker:
Jump over and see if I've covered the bases and improve and vote.
Jeff, the issue creator