Sure you can do it. But it'll cost so much in parts and time, that it would be cheaper and less hassle to sell it and buy a 1.8T.
You would need to change so many parts on your original engine to do it that it would be easier to just swap the whole engine. No matter which way you do it, you'll need an ECU with the correct mapping for a turbo, so that will also mean you need the loom, keys, locks and clocks to go with it.
The cheapest way to do it would be to buy either the full engine, turbo, g-box, ecu and wiring from a crashed car and then swap them over, or to buy a complete crashed car with everything for the swap.
But this would cost you a fair amount.
If you got it on finance, talk to the finance company tell them you want to change your car for a 1.8T, and ask them if they'll let you sell your current car and buy the 1.8T. They will probably do it if you agree to a new finance deal on the new car.
Oh and if you want to see what's involved in swapping a 1.8T engine into a non-turbo Mk4, check out Ashmond's project
http://www.golfgtiforum.co.uk/index.php?topic=58241.0Which went from a bottom of the line 1.4 to a 1.8T.