Simple answer is yes. It's the overall rolling diameter that you have to try to match. If you don't plan on modifying the wheel wells (other than rolling the guards), your biggest issue is the width and offset of the 20" wheels.
The biggest wheel/tire combo from factory for BJ Protege was 17x7.0 wheels with 215/45R17 tires, and ET55 offset. That combination has a rolling diameter of 24.6". To keep to that rolling diameter with 20" tires, you'd have to fit 205/30R20 tires (24.8" rolling diameter). Then find 20" rims that are 7.0" wide, with a ET55 offset and you'd be able to fit them on a Protege without too much issue. Possibly an issue on the rear wheel wells where there might be rubbing depending on ride height.
Finding 205/30R20 tires is not easy. They're available. But not from big name brands. Having such low profile tires you wouldn't want to drive on any damaged roads that's for sure. You'd be riding on rubber bands! Next issue is finding 20" rims that are 7" wide with an offset of ET55. There are a couple of Mazda factory wheels that are 20x7.5" and ET45 off of the CX5-CX9 range. See below for one such example.
20s on a Protege sounds horrible to me, but that's just my opinion. Back when I was researching OEM wheels for my Protege, one of the larger choices was the earlier 18" RX-8 5-spoke wheels, and those seemed like they were at or approaching the limit of what could fit with stock suspension and body. Stock though, mind you. Anything can "fit" with enough modification.
Beyond 18s though, I would agree with theblooms. Don't put 20s on your Protege.
For sure, 20's are a BIG wheel for a Protege. I wouldn't go bigger than 18. My first choice would be to stick with a light weight 16" wheel. My second choice would be a 3rd generation Miata 17" wheel. The Protege is VERY sensitive to wheel weight, and a light weight 16 with a 205/50-16 tire is the best set up. Second choice would be Miata 17 with a 205/45-17 tire.