You would have to adapt the existing connectors to something PROC boards could accept. I'd suggest not chopping off the connectors in case at some point you or a new owner wants to convert it back to the original boardset.
Atari doesn't have a lamp or switch matrix, so you're good there (P3 doesn't support a switch matrix).
I'm not sure if the software would be able to handle the digit displays or not. Out of the box, I think you might be limited to an LCD with P3. I remember seeing some 3rd party work on digit and alphanumeric displays, though.