Technically, it's possible, but it means a really small turbocharger that will peak out quickly (note the 211hp is made at 4300rpm in example above).
Our turbocharger kits for the 2.5i Impreza's looked basically like this:
The dyno doesn't show the onset of boost, but road tuning shows the magic starting to happen at 1500rpm. Peak is reached relatively early at 2800rpm, and it plateau'd till 6400rpm, where the 2.5i's start getting in reach of their redline.
Now - this is not the 2.0-liter BRZ motor! It's just an example. The 12:1 compression, different combustion chamber design, and higher rev limit/available power band means different results and different setups. With the turbocharger up front and right off the exhaust manifold, though, it will probably respond quicker and may get to peak torque sooner.