Don't even think about it.
It's fraudulent - can get you in a lot of trouble, and they can spot it a mile off....
how can it be fraud when the car has got tax and mot left on it
so the car is perfectly legal for the road
its just broke down (head gasket gone)
so thats what the aa are there for to get you home
If you were driving along and the head gasket blew, then it would be within the AA terms of service.
As you ALREADY KNOW the car is broken, it is no longer covered under those terms, and by towing out and "pretending" it has just blown you are making a fraudulent statement.
If it has been blown for any length of time it will be very obvious to the AA that the car has not run recently. There are several options that then present themselves .. including the police and fraud charges
The AA do now react strongly to such matters as all the other members would be paying for your fraud.
Not worth the risk IMHO
but thats just my view...