There are several - "It's bad, don't do it." comments, and they are probably right. That's my first impression, too. But the reason it's bad for the AC compressor to run at low voltage is that the motor needs a certain amount of power, and at low voltage, it takes more current to produce that power. As the current goes up, the heat produced in the windings goes up as the square of the current. Heat is bad for motor windings. It's possible that momentary low voltage sags do not produce enough heat to significantly injure the windings, as long as you get the voltage up reasonably quickly.
I'm not saying the comments are wrong, but I doubt anyone has done any real testing on this issue, and it's possible you are doing no harm at all - at least not to the AC. However, you'd be doing something that has the potential for harm and all that can truly be said is that the system isn't designed for that type of operation.
The gen might not be happy either, although I don't know much about your champ. Gens don't usually like to start at full load. So you are left with the choice of either trying to get into the region the equipment was designed to run in, or doing experiments and possibly busting expensive equipment. :)
