Hmmm, I dont see why they wouldn't do callouts like this, for instance, if, hypothetically you were disabled but were able to drive but unable to climb over the passenger seat to get to the drivers side then you cannot go anywhere, so technically you have broken down. However i dont know whether or not AA just do engines. Try there website, it might give you some idea of what they actually cover you for. Hope you get it sorted soon.
i first thought it was frozen when i went to get into it yesterday morning after a hard frost, but now i seem to think its mechanical the lock turns ok it just cant be pulled open.