I doubt it. The compressor should have an Amp rating on it. If it's less than 10 you could do it. It'll run your battery down pretty quick so keep the engine running.
I just checked the specs on a compressor matching your description on the Home Depot website and it is listed at 10 amps. The thing is, is that at start-up or steady load? When devices like that start up they draw more current than when they are running and that could be enough to blow a fuse.
You'll definitely be running things on the ragged edge either way and could end up overheating wiring on the truck or the compressor and causing some grief. If it was a company truck, and a company compressor, I would try it. I wouldn't do it with my own gear though.