Not much of an upgrade. SOHC + 3 valves per cylinder = FAIL. It's 2.2 L but in N/A form makes less horsepower than a stock 1.8 Miata, though a bit more torque. I couldn't even guess how much more the block weighs. The GT used a tiny schidt-kicker pea-shooter of a turbo and only made 145 hp and 190 tq. By the way that 145 hp peaked at 4300 rpm LOL. Total weaksauce, nothing I'd want in a Miata. You're better off just turbo'ing the motor that's already in the Miata and saving yourself a bunch of time and money.

If you're going to bother swapping in a bigger Mazda 4-cyl, the one that makes some sense is a 2.0L FE3-DOHC swap. Those were used in the 95-03 Kia Sportage and are cheap and fit pretty well once you cut a few inches out of the oil pan and fab up some mounts. It's DOHC and 4 valves per cylinder with big forged rods, well-supported main bearings, piston oil squirters, etc. IOW, it's turbo-friendly and the stock internals are proven to stand up to some decent power. There's a guy with a nice build thread on miataturbo.net.