Yes.
Say you have a Sherman tank with an 8-1 AL which was Recalled and sent to the MHA. In the ensuing RePh your final AFV Repair dr is a "4" so the tank remains in the MHA until it gets fixes or is Eliminated. If the Sherman does remain in the MHA after trying to "fix" it, the AL is Eliminated ("Sorry Frank, got no other vehicle for you to command and do not know if or when another may come available. Head back to the CP and grab a cup Joe. You can sit the rest of this one out.").
Obviously, if the tank is Eliminated, then so is its AL.
If you do NOT possess another Retained Sherman tank (even if you have halftracks and M7 Priests galore) the AL is Eliminated.
If you DO possess another Sherman tank, you may transfer him to THAT tank for use in the upcoming CG Date ("Good news Frank! The Sherman tank, Crazy Suzie, is in need of a good tank commander. I'm giving it to you. Go get 'em.").
During play you will quickly see how little impact AFV's have on this battle (few available as RG's). Coors is mainly an infantry/gun/OBA fight. Air Support and NOBA play minor roles....AFV's seemed to play an even smaller part. Only one platoon of Shermans sent to the island and a platoon of M7 Priests. Most were damaged by mines upon landing and the armor played a minimal role until the last couple of days when two of the Shermans supported the attack towards the tail of the Rock.