You're going to "fill that room up" with sound. You're going to fill an aquarium full of water. It doesn't matter which wall (floor, side, etc) you build from plastic wrap, when that water comes pouring out of the aquarium, it's getting everywhere in the house. So you treat a common wall ... the vibrations get to the roof joists, which rest on the outside wall of the bedroom, and, you have sound in the bedroom ... through the floors, ceiling, attic, places you would not expect. A one or two sided aquarium is rather worthless.
Sound in or sound out. In the overall scheme of things, it doesn't make much of a difference. The isolation techniques used in typical construction are not one-way devices. On the other hand, isolation to reduce sound transmission out of the room is harder to do than the isolation required to prevent environmental sounds into the room (unless you live next to Hobby, Sugarland Airport, etc.)
A traditional metric is you don't want to raise the noise level in an adjacent space by more than 3dB. So if the ambient noise level in your room is 33dB (not unusual), then outside your room, you don't want the noise level to get above 36dB when you're playing your system. The usual sound track is recorded with a dynamic range from 22dB to 105dB (115dB for LFE). By that metric you have 105dB - 36dB is 69dB ... good luck. Even with GG, DD, Clips, Isolation, careful HVAC work, etc, etc, you're not going to get there from here unless the crew building that shell is expert in building isolated rooms. (Just as a reference ... going from 33dB SPL to 36dB SPL is a doubling of SPL.)
Let's go the other way ... ideally, you'd want the noise floor in your room (equipment and HVAC running) to be 21dB (just below the softest sound recorded on a CD, DVD, BD) so you can hear the softest sound without turning up the volume (and making your sound isolation problem even harder). If the ambient noise level in your home is 33dB, then your isolation requirements are 33dB - 21dB = 12dB ... a much easier problem to solve...but, even at that, it isn't going to be solved by half way measures.
Does sound isolation affect in room acoustics. Yes; but, indirectly. You have comfortable listening levels, enhanced dialog intelligibility, you're not running your system at levels upwards of 8 times intended volume (to raise the quietest sound above the background level), running your equipment to distortion and you don't have to buy as many bass traps from Ethan.