No... if Boise State were hosting a tournament, it'd be at Taco Bell or whatever corporate name their pavilion is about to assume.
When Idaho goes to Boise to appeal to the population base of the state, they go to either Century Link (the hockey arena) or Nampa's Idaho Center (really a rodeo arena that also has state HS basketball tournaments). I think Idaho has hosted Boise State once at Century Link, basically because Boise State "usually" refuses to travel to Moscow.
So, eh, it's very likely Idaho's tournament, but just happens to be in Boise. Boise State may not be inclined to play in it.
UPDATE... https://www.bloggingthebracket.com/2017/11/27/16671208/2018-19-college-basketball-early-season-tournaments-events-mte-neutral-site-showcases-thanksgiving
This list doesn't have this tournament yet from what I can tell. What it DOES show is that Boise State will be in the Cayman Islands up through November 21. So I doubt they're turning around back to Idaho to play that fast.