The question would be, which Avaya system? There are a few that could fall in that size category, both "native" Avaya and their adopted Nortel variants... Mitel has some interconnection documentation depending on the systems involved, but it's just a framework.
Both systems should be able to support SIP trunking provided the licensing is there in both systems. The programming side of the 3300 is fairly simple, build a SIP peer, build the ARS and the Mitel is good, a similar process would occur on the Avaya. This would not be integration though, just a simple A can call B and B can call A, not other services would likely be possible.