Six years ago when I obtained a mortgage I tested just this. Correct email and address but no phone number. What happened is that the documentation and all that with the lender was submitted fine without one. And my broker didn’t need one (we used email after our first in-person visit). But once I logged in to manage the mortgage (after a few payments already) it insisted on a number. I put in a null number and it was fine.
This only became a problem when the mortgage was paid off last year and despite getting emails about it, I got a registered letter saying they must talk to me and that haven’t been answering my phone. So I call them as instructed and it was just a “you’re done. We’ll be mailing you documents to send to your insurer. Thanks for your business.”
FWIW: I’ve never personally owned a land line. The last time I ever lived somewhere with one was 19 years ago.