would a back box off a turbo fit a 2.0 sport

 

The Forester XT backbox fit a 2.0 NA Forester just fine, so I would guess that the turbo back box would fit at na impreza just fine.

 

Yes, had Turbo backboxes on all my Sports.
It also depends on what year your car is though,
on the early cars they bolt straight on but on the
later ones you have to cut off the flange and re-weld
it back on at a different angle.