No way. Paulie was dumb, but not stupid enough to kill a guy who at least a dozen witnesses saw him go off on. Look at the caution used when Paulie 1) moved the Russian to Pine Barrens, 2) rapidly left the scene after killing the waiter, and 3) removed the jewelry from Puss. Those are just off the top of my head.

The one standout uncautious moment was when he killed that old woman who was friends with his mother. But even then Paulie had the luxury of having no witnesses since it was a private home.