Yes, it's absolutely feasible. I did exactly that with a simpler version of this (Tic Tac Toe, and console only, no actual visual interface) but it worked pretty well.

The main thing is having a good idea of what the overall program structure will look like. If you have that, I think you can go pretty far with it.

Btw, in case anyone wants to see what working like this may look like, I recorded myself while doing that little experiment: https://youtu.be/TBMQIDMwI5E