As long as it's not a load bearing wall you are fine, but most outside walls are load bearing walls and with how lumber is graded and the movement of the grain cutting your studs in to twin 2x2's will really weaken the wall.
Why it works for sound deadening is that most partition walls where you want sound deadening are not load bearing, I've seen some partition walls in houses built out of 2x2's... not the best idea, lean on the wall and it can bend and flex.
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