Hey, Yes you do officialy qualify for a rocket scientist with that theory, but ill break down the problems with it and the idea of a turbo.
--first off it is completely possible to turbo the gts. it has been done by XS engineering. currently it is a shop installed kit only by them.
you are absoluetly right about the compression issue but there are no aftermarket pictons available to lower it, however there are alternative solutions installing a thicker and stronger headgaskets will lower the compression to a more turbo friendly level. currently the XS kit runs 7.5 pounds of boost. this low boost is completly possible in a high comression engine as long as you have a good boost contorller and wastegate to tune the boost to a reliable 7.5 (boost spike are bad)
what XS did is incorperated the laregest 3 core intercooler i have ever seen into the front this keeps Intake
air temp down thus denser air is easier and safer to fit into a high compression engine.
-other problems not thought of when people talk about turbos is that you will not pass emissions it eliminates the cat because your old header is now an exhaust manifold to feed the turbo and a down pipe that connects to the celica's already tiny mid pipe. (the GTS cat is virtully part of the header)
you have to tap your oil lines as well to run oil to the turbo to keep it cool. along with this comes adding a oil cooler to keep the temp down as it leaves the turbo and an oil catch can to keep the flow positive. after you have done these mods a turbo will work but work badly in the celica. SOOO now you have to buy a fuel management computer (Apexi S-afc) for increased fuel dilvary to keep up with the added air your are sending to the engine. to do this you need a new intank fuel pump and a rising rate boost sensitve preasure regulator... but wait theres more because almost all fuel regulators work on a fuel return line and the celica doesnt have a fuel rturn line. you now need to get a new highflow fule rail and then tap the end and run a return line back to the loop. along with the rail you might just need some higher pulsed injectors so more fule can be injetced into the pistons.
-- now that you got all the fuel and air into your engine and have it all matched (tuning required) you need to upgrade your ignition start with denso irridium spark plugs and except NO substitute as these are the best for any toyota (read your manuel for details). With the new spark plugs you have to make sure spark is consistant or the engine will not knock and ping so you need to add a new coilless ignition (HKS twin power) also except no substitutes.
---- OOOO K no that we have that covered you have 1 last mod to do and that is Cam timing gears so you can advance or retard your timing. because you have a turbo and more air and more fuel and more spark are happening faster you have to advance the timing so the camms will open the valves at the right times for optimal flow of Intake
and exhaust gasses. (the better the engine breathes the faster your car will be) i assume at this point that you have an exhaust but now is the time to check that it is 3inches all the way through because you DONT want back preasure getting to the turbo. oh by the way you will also need a clutch cable to handle that puch power and LSD to keep the power on the ground and from ripping the front of the car off.
- all in all the venture will cost you a total of about 10g's with EVERYTHING turbo and piping shit will cost you about 5G's.
soo now you know and now you can hate me for taking your and my dream of a turbo celica and just stomping the hell out of it because i know 10 g's for a fast car that already costed 25g's and i could just got my self a trans am... but wheres the fun in a f'n american car.
hope you learned some thing today