Avaya seem to sell proprietary handsets as well as IP ones. Asterisk can only work with handsets that follow open standards. I can’t actually quickly confirm that the Avaya IP phones use open SIP standards. Also, although I don’t know if this is the case with Avaya, some SIP handsets require provisioning servers that are only available as part of a PABX from their original supplier. In any case, you need to identify the handsets that you are trying to interface.
A quick Google didn’t bring up any reports of interfacing Avaya phones with Asterisk. Whilst I can’t be certain that this is not possible, I think you have to consider that as a possibility.
Incidentally, please note that this is a peer support forum, so there is no guarantee that you will get a definitive answer.