https://bg.battletech.com/forums/index.php?topic=78634.msg1860313#msg1860313No the BAs can still ride the damaged mech.
So depending on the faction, you could have Battlearmor personnel whose main orders are to jump on a Battlemech to provide the extra armor points as needed.(Pity Battlearmor can't use Hardened armor per Tech Manual corr 6th edition, p169)