No. A couple weeks ago when i was drywall mudding my room I thought of the idea, and i decided to try and find out immediately rather than ask the internet and wait. I don't recommend trying.
First there were immediate delivery problems, hand tools suddenly starts looking alot more practical. The plaster is far too thick & heavy for the gun to shoot. When it does shoot some, its random spurts of gobs and most of it didn't make it from the gun to the wall. I may have fared better if i had a conventional spray gun (high pressure low volume), i had a common low pressure high volume gun.
Second problem was nearly as immediate, and could make you cry. Paint guns are designed to use paint, that if you leave in the gun it doesn't dry and clog the gun in 20-30 minutes. Paint also has solvents that clear the gun for you if it did dry in the gun. Plaster sets in about 30, and there really isn't a solvent to make dried set plaster go away. So basically you have to mix, spray and clean it all out of the gun in 30 minutes, or you won't have a functional paint gun anymore. It didn't make me cry because I had a feeling my gun will break and i had one of those so-inexpensive-its-nearly-disposable harbor freight paint guns.
If you use a slower setting joint compound it wouldn't ruin the gun, but it won't spray on the wall like paint either.
IF you have a conventional high pressure, low volume paint gun though, maybe lots of pressure is all you need to make it work. Slower setting compound will give you ample time to clean it all out before it sets/dries.