The Thermo Switch in the Radiator is not connected to the circuits related to the AC.. period.
Assuming the AC circuits are all working properly, the Thermo switch can be bad or unplugged and the AC will work just fine. Thus, basically they are two separate systems using some of the same devices, namely the Fans.
Simply put, if something in the AC circuits has caused the Fans to quit working, it will not affect the function of the Thermo Switch. My guess is the Fan Control Module (FCM) has gone kaput if the AC compressor is not kicking in.
When you turn on the in-dash Fan and push in the AC button, does it light up?
As for running the fans constantly, well, if you were on a cross-country trip in mid-July with the AC on, those fans would be on continuously. So, running them all the time should not hurt anything.
EDIT: For engine cooling purposes, the fans out front hardly ever kick on while the vehicle is up to speed. There is more than enough air flow to maintain cooling needs. The fans are primarily for stop and go as well as AC function.
EDIT 2: The Thermo (Coolant Fan Control Thermal Switch) switch on the radiator turns on the fans at Low Speed directly (not thru the FCM) based on coolant temp in the radiator at the switch. If the temp is high enough (based on the Coolant Temp Sensor in the coolant flange on the end of the head), the ECU will send the signal via the Fan Control Module to turn the fans on High.
So, I feel quite certain your "no AC and no Fans" is due to an AC circuit issue. Also, not mentioned above, the outside Temp sensor can be an issue. It is located below the windshield on the driver's side behind the cowl.... sort of hard to get to. If critters have chewed one or both wires in two, the AC system will not operate (ask me how I know).