Man, anything can be done... the question is how much time you have and how much money you want to spend.
Can you add compressor on 2.0? Yes, you can.
Can you use 1.6 equipment, well, technically you could, but it will be too small.
Now, the rest of it.
Let's start outside, meaning room in the engine bay. Modifying exhaust, adding intercooler, routing air ducts, equipment (computers), and programming. Not to mention fuel delivery.
Then, inside - would the head take it? Would pistons survive? The most crucial - connecting rods - early 1.6 T GDIs had tendency to bend them.
so many parts may need to be reinforced or replaced...
All in all - you are looking on months of work and probably the result will be very unstable car. Side effect - you will spend thousands of dollars and will never recoup it when selling the car, because the market is very low for such heavily modified car.
Either swap 2.0 T from KIA or Hyundai, or get Forte5 SX, or get a 2.0 T car.
What I would do?
I would get 1.6T GDI and tune it. Nothing else (just KN drop in and HKS spark plugs). It will act very so much like 2.0 T, but with a quicker spool due to twin scroll, while at the top it will be weaker than 2.0 T... but not so much (I mean, after the tune).