Safe to test circuit breaker is working by overloading it?
A breaker is designed to safely trip out on overload. That being said, anytime you have a breaker trip out on overload you are doing some damage to a breaker and it actually changes some of the breaker specs and properties. Also as mentioned all breakers have time curves that trip breakers under certain conditions. For example if a 20A breaker is loaded to 25A it may take up to 2 minutes to trip, where a direct short causes an instantaneous trip.

The best way to test a breaker in the field is to use an amp meter and it should be sophisticated enough measure peak, constant and average amperages of both the ac and vacuum. It will usually trip at startup so measure the peak at the ac startup. Then measure the vacuum startup and do the math. If you have the breakers time curves you can check on how long the overload will hold.

If you really want to make sure the AC is the only thing to be used on a particular circuit. Is first make it a separate circuit for that equipment only and use a simplex outlet instead of a duplex.