PATS system is only for fuel control so can't see new PATS keys having anything to do with the Radio.
Battery however is part of the radio system, the "go juice", lol.
On the newer vehicles, 1995 and up, you need to disconnect the battery before charging, the sudden voltage changes and electrical "noise" generated by battery chargers can cause problems.
Do you know if your son used the Ford Radio power wire, if not then those fuses wouldn't matter?
Did the radio go off with the key?
Or could it stay on?....direct wire to battery
There is, on some models an Accessory Delay Relay, this allows you to use the power windows and Radio after key is turned off, but relay will open if a door is opened, so radio would go off.
Do you remember this "option" being on your truck?