Many do, but it depends on where the actor is in their career. Some performers prefer not to be in New York in September, rehearsing four weeks to give six performances for astonishingly little money. If you go to somebody who has the attitude of "I'm a star: Your NYMF show needs me more than I need it." this could result in getting jerked around. Others, of course, relish the idea of creating a role in a new musical. It's something I was fairly naive about, but a good casting director tells you which is which.
And part of it is just the nature of NYMF too since each of the show's six performances are spread out over two or so weeks, and at different times. Depending on people's "day jobs", it may not be that easy for them adjust their schedule.
Conversely, the early fall season is an ideal time for The Fringe and NYMF since there are usually a bunch of actors who have just gotten back from summer-stock gigs. And since they were working out-of-town, they weren't able to audition for some of the other productions going up this fall. And in regards to Broadway shows, unless it's trying out out-of-town, most shows wait until the Spring to open. So, some of those "Broadway Babies" may be available also.
And judging from some of the work I have lined up for September and October, this fall in New York City is surprisingly busy in regards to "big" auditions. (And it was already an unseasonably busy summer this year for most casting agencies.) There are lots of possibly-buzz-worthy productions - both here in NYC and elsewhere - that will be auditioning actors over the next couple of weeks. Additionally, a couple of currently running shows have their regular "6-month calls" coming up too - and there are some known openings available for various projects. I have a few friends who are keeping themselves "open" in order to be available for auditions. Yes, that can be risky - to work, or not to work - but that's the Actor's Life.