It has been proven the answer is 'no'.

Now, aside from issues with the climate control panel in the console, there are some things to consider.

First, the design of the climate control is such that if you turn the fan off, the A/C clutch disengages. This is because, if you keep the pump running with no air flow over the evaporator, system pressures will go out of range, the A/C is designed to MOVE HEAT, and if there is no air flow over either the evaporator or condenser, then no heat can be moved. So, if the climate control 'thinks' you turned the fan off, it will disengage the clutch for the A/C pump. Can a bad fan resistor cause this? I do not think so, the climate control outputs a .5 to 8 volt signal to the 'fan resistor' which the 'resistor' turns into a pulse-width-modulated 12 volt feed to the fan motor. THere is no "going backward" with any information on the status of the fan for the climate control to go on. So, a bad fan resistor cannot cause the clutch to disengage.

Well, maybe. There is a sensor (two acutely) on the evaporator that tell the controller what the temperature of the air is passing the evaporator. Perhaps the climate control will lock out if it does not like the temperature reading it is getting - due to the fan stopping. Replace the fan resistor - it's cheap and easy.



There are some other things that can disengage the clutch. The "A/C heater control module" directly connects to the clutch, but the module commands the clutch to engage and disengage based on 'permission' of the ECU.

When the climate control tells the clutch to engage, it first tells the ECU it is going to do so. The ECU responds with "go ahead" and also opens the throttle a bit to compensate for the added load.
The ECU will refuse to allow the A/C clutch to engage in a few scenarios:

1) The ECU senses a high engine temperature (the gauge should show this).
2) The ECU senses that the driver is asking for a lot of horsepower (like passing, etc; the ECU will disengage the A/C clutch to provide more HP for acceleration).
3) The ECU has detected some sort of issue with the engine cooling fan. (The little "radiator" or "low coolant" light should be on, but I"m not convinced that ALL such errors light the light.)

Just keep in mind that issues with the car OTHER than the A/C can stop the A/C from working!

As to the A/C itself, you may have a defect in the climate control circuit boards themselves (which you have obviously suspected, based on your post above). Also, there is at least one pressure sensor in the refridgerant system that will stop clutch engagement if the pressure is not what the climate control module wants to see. THis could be a bad sensor, a bad climate control circuit board part - or actually bad pressure.