I don't see why you couldn't, but that also sounds extremely inconvenient. You can always have a dumb phone and a smartphone. Just don't set up service for the smartphone. You can still use it on wifi. If you end up needing to get a new smartphone later, because it's no longer supported or whatever reason, you can always get a cheap low end phone.
I'm assuming you have a smartphone now and it seems like having both devices is the more convenient option.