Is a YMAV essentially the first day you can be assigned to a new unit? Can you PCS prior to the YMAV?

Not to a new unit, to a new post. You can always be moved within a MACOM as long as it's within the same MACOM. That can even be used to reset your YMAV.
You CAN PCS prior to your YMAV, it's not like a DEROS where it's a hard and solid date. It's more like you WILL be evaluated for movement about 7 months prior and the first day of movement will he the month after.

However, there are plenty of times when a branch may move you. For instance, a special assignment, a broadening assignment, or you've finished your KD time and it's time for the CCC.