MLV can easily install between layers of drywall while you put up new walls. You can either stick the sheets in the open space to either side of the studs or place some directly between the studs and the walls.
MLV will always add mass to the surface you place it on, which helps prevent sound transmission. Decoupling a wall from its studs using MLV turns the wall into a limp mass barrier that absorbs more sound than a wall directly on its studs. The slight cushion softens the impact when a soundwave hits the wall, improving its soundproofing performance.