There are some guys running GTP's on here with some serious mods and running 11's in the 1/4 mile, which is very respectable compared to any street car. You can spend alot of money on your GT to make it faster, but I think it's best the way it is closer to stock. It's a perfect all season commuter and touring car that is very reliable.
I have a few sports cars, a Porsche with a modded V8 and 600hp, but I knew the stock engine/drivetrain and engine could handle the increase to 600hp without suffering breakage problems; a newer bmw 5 series with a turbo system and 500hp but I also made sure that the stock engine and driveline could handle the HP increase without crapping the bed; and a toyota mr2 turbo (close to stock because I feel the transmission can't handle abuse or anything past 270hp), and these cars are all fast cars, but each do different things better than the others. If drag racing and times are the big thing for you, you could spend less by keeping your car stock, and buying an extra car that is popular with pro streeters, like a pre-owned mustang V8, or firebird with LT1 and likely a few other good cars too. Buy one below the snow belt and then rust won't be a problem.
From what I am seeing, you can't do alot of mods to a NA GT to go much faster without spending alot more cash to keep the rest of the car reliable.