Zoom Phone integrated to Avaya IP office

Not personally, but search for BYOC bring your own carrier and you should learn how to make a sip trunk between Zoom and your PBX. I could be wrong, but I think this is technically feasible. Good luck. 

Yes. You can do this using BYOC and an SBC. You will build a SIP trunk from Avaya to SBC. The SBC  is connected to ZP BYOC.