No problemo. Walkway airside. IIRC, WN even had a few flights going out of T1 - not sure if that's still the case. TSA does not care at any airport. I have used BP's for term A departures at IAH to get into term C for the president's club. Done similar things at STL, SFO, etc - all cases where the terminals weren't even connected airside. The most they will do is warn you you're going through through the wrong checkpoint for your flight - but they won't prevent you from going through.