I have done it.
With semi-autos: you get one shot. Never a second one. The slide can't move inside the pocket, and if it does, the fabric will jam it up and stop it from going back into battery.
With revolvers: you can fire multiple shots. Your hand will feel warm, but you won't get burned unless you hold the gun stupidly. If you have practiced shooting from retention position, you may be able to hit a target at very close range from inside the pocket. You probably won't be able to do it well or in a repeatable way, and you probably won't destroy enough jackets to get really good at it. It's fundamentally different from firing outside the pocket in the same basic shooting position, because you don't have the benefit of seeing the gun out of the corner of your eye, and because the shape/feel of the jacket pocket changes your body dynamics a little.
The biggest drawback is that if you are carrying in a decent pocket holster -- which you really should! -- you'll have to pull the gun out of the holster before you can fire.
I would do it if I were rassling with an attacker so could go for a contact or near contact shot. Not otherwise.
My personal website: Cornered Cat