What you said isn't far off. However, I disagree with the poster who speculated that foul trouble would be the primary repellent to Nolan and Brimah playing minutes together. That's over-thinking it, IMO. If Nolan proves to be our best option at the four, he's going to play at the four, regardless of how valuable of an insurance policy he is at the five. Great coaches always have contingency plans in place in the event that foul trouble becomes an issue. But throwing your hands up in the air and keeping somebody on the bench because you're afraid both of your big men are going to foul out is not a solution (and it's not a scenario that is likely to occur, either). Plus, we don't know if Facey can play the five. We all thought he might play some five his freshman year, and he didn't, but that doesn't mean he won't this year.
To answer your question, basketball is an interesting sport in that every lineup configuration is dependent on versatility. Obviously, the five players who are on the floor might not be your best five players - our best five players last season were Boatright, Napier, Giffey, Daniels, and Kromah in some order, but they very rarely played together. Being able to modify your game to fit the personnel grouping is a skill that I think gets overlooked in basketball players more than it should be - Alex Oriakhi did not have this skill. Phil Nolan does have it, I think, on the defensive end of the court. I wasn't sold on Nolan as a basketball player until I watched him shutdown Adriean Payne in the elite eight last season. He's privy to rotations at multiple positions, he moves well laterally, and if it's true that he bulked up over the off-season, he should be more equipped to bang with centers and avoid foul trouble than he was last year. Truthfully, I think the guy is more of a four by nature who was forced to play exclusively the five his first two years here by some combination of roster constitution and offensive limitations.
Which brings us to the big question: is Nolan a skilled enough offensive player at this point in time to share the floor with Brimah without destroying our half-court offense? Everything we've seen from Nolan would indicate that he's not. His jump shot is unreliable, he's probably an average athlete by UConn standards (the national championship game last year being exhibit A), and although his foot work in the post is impressive, he doesn't have a soft touch down there.
If you're going to play the four successfully in the half-court, you have to either have one of the aforementioned skills, or you have to be a gifted interior passer. Louisville was able to construct a passable offense in the year they won the title in large part because of how Gorgui Dieng evolved as a passer from his sophomore to junior year. It gave them the luxury of playing two big's - Dieng and either Harrell or Behannan - at all times, which brought their defense to near unprecedented levels while maintaining an efficient offense. Now, I don't think Nolan is capable of a Dieng like jump, but if he's able to work out of the high post in some capacity, continue to improve as a screener, and hit enough 15 foot jump shots to keep defenses honest, UConn may have a shot at replicating something similar to what Louisville had that season (by similar I don't mean equal, but you get the point).