It's been done.

Unfortunately, the main issue that arises is that you're adding a lot of heat into the intake tract, and usually the supercharger is in line after the turbo, so the efficiency RPM range is about the same as if you had the supercharger running at higher boost all alone.

On a 4 cylinder, I would just stick with a turbo. I've never been impressed with supercharged 4 cylinders. On engines with more cylinders, sure, superchargers/blowers are great for making power and simplifying plumbing issues, but turbos are generally much easier to tweak to generate more usable power across the band.