Yeah, you can super/turbo charge anything you want. It just depends on how much you want to spend/work.
FWIW, my opinion is that you'd be better off money and work wise by selling your LS and then buying an XR7. It's not like they're all that expensive or hard to come by. Usually some listed in the classifieds here, and if not then there's usually several listed on autotrader
If you insist on your car, and I can understand that, then I would suggest getting a Super Coupe or XR7 parts car since you'll need quite a lot of items from the computer to the engine bracketry, to the trans. Far too many items for trips to the salvage yard. You could probably buy a complete broken SC for half what it'd cost to buy it piece by piece from a salvage yard.