Actually went to look up what the qualifiers for the NY6 Bowls were and it looks like this:
"Rose Bowl — Big Ten #1 vs. Pac-12 #1
Sugar Bowl — SEC #1 vs. Big 12 #1
Orange Bowl — ACC #1 vs. SEC #2, Big Ten #2, or Notre Dame
Cotton Bowl — at-large or "Group of Five" (committee selection)
Fiesta Bowl — at-large or "Group of Five" (committee selection)
Peach Bowl — at-large or "Group of Five" (committee selection)
The highest-ranked champion from the "Group of Five" conferences (The American, C-USA, Mid-American, Mountain West, and Sun Belt) is guaranteed a berth if the group's top team is not in the playoff.
The remaining five at-large bids are determined by committee rankings."
So it appears. At least in theory, that multiple G5 teams could go to NY6 bowls in those at large spots if they were ranked high enough and chosen by the committee that way, but in actuality that would be a tall order. I imagine both teams would have to start the year in the top 25 and proceed to either go undefeated or close to it. UH with one loss was only able to climb to #18? But interesting to see it's technically possible.