The whole point of the Big East expanding(if it indeed is interested in doing so) is to gain sufficient strength and stability so that it can become the ACC's bowl game partner similar to what the SEC, PAC-12, BIG 12 and Big 10 have done. So yes, it will something like the Orange or analogous.
But let me reverse the issue. BYU's tie in is the armed forces bowl. Its a bottom 5 bowl dude. Share for me the scenario where their access to bowl's can be ANYTHING but enhanced but joining a conference.