There is no replacement for displacement!
A turbo'd 4cyl will produce only a little bit more HP than a stock GT will. Most of the guys who turbo their GS do it because they like their car, don't want to trade up, and/or like the lower cost of maintenance. The GS is far cheaper to maintain in terms of replacement parts, fluids, and even gas, but the cost to turbo will be the same.
In my opinion, I'd say trade up to a GT and go from there. The cost to turbo + fabricate said turbo is going to be in the $6000 range (from what I've heard) and if you're going to invest that much time and effort, you might as well get the performance model. but I'm a little biased. Really, at the end of the day, do what you want to do
Its your car, after all. Plenty of 4Gers have turbo'd their GS, I'm sure plenty more 3Gers have too.