I suspect the airport will stay open, and the Saudis won’t leave.
What you won’t see is reports that Americans are there with the Saudis. The unit I went to Desert Storm with, which in peace time is 75% civilian contractors, trains and deploys with Saudi military forces. The Army is most likely replacing the civilians with volunteers like they did in Desert Storm. About 150 Americans, O-4 to E-7 with each Brigade.
In the sense that a win for the Saudis is a strategic loss for the Iranians, I think this could be a good thing.