It would probably work fine. I'm not familiar with that specific compressor so I can't provide any details about the quality or the sound level, but as far as just powering an airbrush it should be fine.
It will most likely have a pressure switch on it that will turn the compressor motor on as needed. When the pressure in the tank drops below a certain point it will come on, when the pressure rises to another point it will shut off. The low cuton point will probably be around 90 - 100 psi with that compressor, so for an airbrush you will have a lot left. To keep the sound to a minimum what you'll probably want to do is let it charge completely, then manually turn the motor off. When it gets down to where you can't paint any longer, turn the motor back on and let it refill.
I have a 6-gallon tank on my compressor, and while I've never actually timed how long I can go, I'd say I can get at least 30 minutes of solid painting.
HOWEVER ... since you already have a compressor, why not just go to Sears or somewhere and get an air tank. They are around $30. Get a regulator for around $20. Air up the tank, paint until it dumps, then fill it up again. Basically the same thing as using a compressor in "Manual" mode.