Harrison used to have THS on its non-con calendar back around 2020-2021, so it's not a foreign concept.
If I were the Sagamore though, I would hold off on grabbing the Terre Haute schools as I suspect they might have better options; especially if someone like West Lafayette joins. With that, you'd only need a couple of other teams to make an 8-team conference, and you could almost afford to be pickier at that point. I suspect that the NCC, which claimed it kicked Harrison and McCutcheon out due to travel and "competitive balance" will likely turn their sights on Jeff once they realize that they look just like the two folks they kicked out. Jeff might not be too far off from being #6 or #7. If West Lafayette joins and Jeff's a potential, I suspect the TH schools would be in the running only if the conference wanted to get to 10 teams ... which I'm not sure they would want.