To directly answer your question: No. The 2.0 is a Nu engine, and the 1.6T is a Gamma II.
To explain in more detail. There is little you can do to that engine, performance-wise. And if there is, the Dollars-to-Horsepower ratio is abysmal. At least it's the GDI head and not the Atkinson head, but Nu is an undersquare engine, so, it is tuned for driveability and broader torque range, and you can't coax more peak HP out of revs. You'll spend a lot of money to get up to maybe.. what... 190HP? 200HP if you're lucky? You only have 2L of displacement to work with, and the cost of adding an aftermarket turbo kit is pointless when Hyundai has other engines that just mount right up. Including the Theta II N engine itself. Bet you could pull a Gamma II 1.6T from a wrecked car for not too much money.
The easiest thing to do is just do cosmetic mods and be happy with it. But you want more power, most people will recommend you just trade it for one of the turbo cars, and that's also because they are all still too new; with the oldest 1.6T production vehicle being the 2016 Tucson. The origin of Sport Compact cars, was that they were inexpensive cars (Civics, etc) with weak economy engines that could either be swapped with more powerful engines from other vehicles or had a custom turbo designed and tuned because they had no other options for more powerful engines without seriously modifying the front sub-frame, or the entire front clip of the cat itself. Back then, Honda wasn't selling us a powerful Civic Si, etc. Or we got de-tuned versions of engines that were more powerful in other countries (example: Mazda MX-6 2.5 V6 was 200HP in Japan, but only 165HP in the US). That is not nearly the case any more - so someone buys a cheap Elantra SE 10 years down the road, and they ask about making it FAST, the first thing I'll tell them is to find a wrecked Veloster Turbo and pull the engine and ECU out of it. And I say VELOSTER, because the Veloster actually gets the e-Diff TCS programming. The Elantra GT Sport/N-Line, do not.
