The burning of the powder should be mostly contained within the gun. Along with the noise, burning powder is dangerous to human flesh for the obvious heat reasons - that is why it is important for the breech to stay shut for a little while (a fraction of a second) while the pressure of the burning gas drops to safe levels.
In any case, the energy of from the burning powder mostly goes into accelerating the bullet as long as the bullet is still in the barrel. I’m exaggerating somewhat - I’m sure inside the barrel it is quite noisy, but the barrel wall dampens that sound pretty well. The main noise comes when the bullet leaves the barrel and all the powder spills out into the air to burn pell-mell. This is why guns get so much louder when you cut down the barrels - an M16 (with a 20" barrel) is pretty loud, mainly from the sonic boom; a CAR-15 (with a 10 or 11.5" barrels) is freakishly loud, partly from the sonic boom but mostly from all the powder burning out in the open. In other words, if you don’t use the energy to accelerate the bullet, it will become sound energy. According to the 1999 Gun Digest there is a derringer (with a 3" barrel) chambered in .223 Rem. - pretty much the same round that the M16 and the CAR-15 use. Please warn me to leave the county if you want to fire one of those.
Some suppressors, as mentioned above, work by dropping the bullet to subsonic speeds, but many also work just by absorbing the sound of the externally-burning powder. The unused powder just burns up in the spaces between the baffles.
So I think the short answer to your question, Jman, is yes, powder burning does make a lot of noise, but it can be effectively dampened by a few centimeters of metal, whether that metal is the barrel, the chamber wall, or suppressor baffles. A good suppressor can make the noise of a .45 comparable to that of a .22 (or the noise of a .22 comparable to that of a twanging bowstring, so I’ve read).