It is possible, it could work on a simple principle sort of like a gas valve similar to the type on a pulsejet engine (i have built some before)
Here is one concept I thought of while reading this post.
As you can see though that the temperatures would now allow this design to be a fully automatic weapon because the heat generated would melt a plastic ball to the barrel, the balls in the loading unit would also melt from the heat.
The reason a paintball is not affected by the heat is because of the liquid content inside, however if the C3 was a fully automatic weapon this would quickly change.
How you ask, well think of it this way, youre camping out by the fire pit, take 2 styrofoam or plastic cups and fill one with water, put them both on the flame and see which one gives away first.
The membrane of the cup with water in it is cooled down by the liquid inside therefore the flashpoint of that cup is much higher than the cup with nothing in it. the C3 works because the oils and food coloring insice the plastic capsule cool the capsule enough so it does not melt, and since liquid has a higher boiling point than plastics flachpoint the membrane stays cooled down enough to get the ball out without any melting.
If the C3 was automatic then the heat generated by constand auto fire would be so high that the metal chamber and breech would be red hot, this would damage any paintball or plastic airsoft ball that would sit there when you took your finger off the trigger.
I vote we stick to AEG's, they are just as practical and charging a battery is cheaper than a $3 propane tank, they make no heat and well...face it, they work.
I agree it would be cool to have a more realistic gun but this would require a non heat gas operation, so you'd be going back to an auto GBB which is much less practical than an AEG because youre limited to one of 2 things, a small amount of gas resulting in less shots and crappy FPS or a hose coming out of the gun.