The other side of this coin has been tossed around extensively on Pontiac Grand Prix forums, that being "Can you put the 6T## transmission in a 3.8L Grand Prix?"
The answer is overwhelmingly what you received above, "yes but what a headache, your better off working with what you have."
The key points are the same though:
- Need to make custom mounts/move things around.
- Too much power from the 3.8/the six speed isn't rated high enough.
- You can achieve better results with a cheaper easier modification.
- Shift timing.
If you do decide to go ahead with the project keep this in mind: The 6T## transmissions are rated at max 315 HP/300 ft lb torque, the 3.8L engines (L36/L26) can produce better than that naturally aspirated, though out of the box they are rated at 205 HP/230 ft lb torque. You'll actually have to modify the 3.8L to get what you get from the 3.5L out of the box.
As to the turbo issue... The W-body crowd has had the 3.8L in roughly it's current incarnation since 1995. Some of the engines have been successfully turbo charged, but far more attempts end in destroyed engines and incredibly thorough wastes of money and time. I expect that roughly the same thing is in store for the 3.5L/3.9L, years until the proper formula is achieved and it will still end up better left undone.
The IVVT (infinitely variable valve timing) and offset bore are the main culprits in problems with boosting the new GM engines. The IVVT adjusts the timing of the valves equally in order to optimize performance, so when you apply the additional air from a turbo the engine ends up running lean and killing itself trying to re-optimize the fuel/air mix. With the center of the cylinder bore being offset from the camshaft and the camshaft itself constantly changing position the elevated compression becomes an issue for the piston rods where applied stress is concerned.
The LX/LZ/LY engines are remarkable in that, for the first time, Pontiac enthusiasts have an engine that takes care of needs for added effective compression without using additional parts (turbo/supercharger). All in all the engine your car has is more than capable of pushing the rest of the drive train to its limits if you make smart modifications.
End advice: Modify fuel system (wet shot), tune, remove weight where you can do so safely, and tune again (after every significant performance modification).