I've done a TYA contract through Theatreworks. I already had my card, but 2/3 of my cast got theirs through the show, and many others (outside of my show) I know also did. My experience with TYA is a little different since it was a tour, but I think, if you feel ready to join the union, that this is an excellent way to get in. The upside is that a lot of companies who run under the TYA are willing to hire non-AEA SMs with the idea of you getting your card through the job.
From my vantage point, I approached working the TYA contract as I would any other contract, learn how the rules work (and there are differences from other contracts) and go from there.