While I'm sure that some noise could be cut down on relatively easily with some sort of baffle system to shoot through, even with a big enough hole (ie the tires lined up in a row would present a large apperature) that would allow for the barrel and the sights to be inserted, there is still the problem, I assume, of the sonic boom of a supersonic bullet. Mind you I'm not stating this as fact from personal experience, I'm just assuming. Of course you know what that does for you and me...
I have shot .22 rimfires through a series of three 12z15x24 (approximately) boxes, just boxes with large (about 5 or 6 inch) oval holes cut at either end, with the muzzle in the first box, and normal report was greatly diminished. Something bigger (ie a .38 or a .44 handgun) would have moved things around with the muzzle blast (again, an assumption) It's a thought I've often pondered, but not really experimented with beyond the boxes and a .22. What I didn't say, by the way is that the shells were subsonic. A Ruger single six with a 43/4 barrel was significantly louder fired through the same box set up.
Jamie