Looking to plug in my Aerostar to run the a/c to precook the cabin. POH doesn’t give much guidance on the subject.

Is there any issue with the amps of the gpu? Does the wiring and relays control how many amps are used?

Precook or precool? The electric AC in the Aerostar is supposed to be charged with freon until the electrical load is at 55 amps. You can't fully charge the AC to a clear sight glass or it will pop the circuit breaker. Most FBO apu's will start a turbine engine pulling an initial load of 1,000 amps and should easily be able to maintain 200 amps at 28 volts continuously so no problem running the AC at 55 to 60 amps.

Unless there is some specific procedure indicating otherwise, this is commonplace on most aircraft with electrically powered A/C. Living in the south, it's practically a required item for my Mustang

First thing I do on arriving at the FBO is connecting the GPU and fire up the A/C. Also nice to allow the avionics to connect, sync up, etc while I am doing the preflight.