Let's explore this one. I like the question.
Assumption: carb, no "kick up" solenoid.
That being the case, the engine will either maintain the same RPM or stall (if the idle is insufficient to support the extra load).
The amount of gas being drawn into the cylinders (for given atmospheric conditions) is based solely upon the volume of air being drawn through the venturi. That volume of air will remain the same, since it's based solely on the idle speed and the carburator settings. Added load does not automatically drop the idle speed.
I believe we're looking at the problem backwards. The engine doesn't need more gas when the compressor is engaged, it simply stops wasting so much. In essence, it's operating inefficiently at idle with the compressor not engaged.
If there were insufficient gas being drawn in at idle to operate the added load, the engine would simply stall.