absolutely could. And the higher ups would sign off. With Grimes' experience at BYU, those hurdles could absolutely be cleared. Those hurdles could not be cleared though if Tom wanted to bring in Jimbo or Urban or Dabo. The LDS (card carrying) requirement is not a hard and fast rule but Tom probably views the hurdles that would need to be cleared to be too great for everyone but a handful of non-LDS coaches (effectively making it a hard and fast rule for practical purposes).
I think basically that coach will have to have coached at BYU before in some capacity. They'd need to have shown that they know and understand some of the unique things that go on here. You can't just be told about them.