fire suppressor,
Yes, it will fire. But as always, if you carry a "pocket-gun" do NOT carry ANYTHING ELSE in the same pocket. ONLY the gun. And consider a pocket-holster than orients the gun in the same way inside the pocket so you always know where the grip is every time you reach for it (no "surprises" or fumbling for the grip)!
As for your clothes catching fire, it's possible, but if you need to be shooting your gun, then you have MUCH more serious issues to be concerned about than your clothes!
...kind of like the people who worry about re-holstering their guns, that they have trouble getting a gun back INTO its holster after drawing it -- forget it: You really don't care about getting a gun INTO a holster, you only care about getting it OUT. If you survive the encounter, you've PLENTY of time to get it back INTO the holster...if you don't survive then it doesn't matter, does it.
So your pants or sport-coat MIGHT catch fire -- you're still alive, buy another. Or go through the BG's pocket ("just looking for identification") and have HIM pay for your replacement clothing -- and maybe even extra $$ for going out to dinner or whatever. Works for me.
;-)