I feel like boxing would give you the greatest edge/return in MMA, as it's most competitors' greatest weakness, and thereby the best area to exploit. The reason it is their greatest weakness is, imo, because it is the most subtle and therefore most tricky/difficult art to pick up. It's the hardest to "see" what's going on, and when you're good at it you can gauge wide open opportunities that others have little to no idea are even there presenting themselves.
Wrestling is really awesome too, but training defensive wrestling is a lot easier and quicker, apparently, than "defensive boxing," which- you pretty much just have to be good/great @ all around boxing to be good at "defensive boxing." Defending against boxing is the most difficult task for boxers themselves. *Wrestling is good at foiling pure boxing, but if both guys are decently versed in wrestling, it cancels out (in MMA), despite a significant skill differential, and goes to the guy with slightly better (or much better) boxing.
I know this post is awkwardly worded (I just read it to myself) but I think you see what I'm saying. I think dedicating yourself to boxing (only) for a period of time until you are impressing your coach with it would be the biggest payoff for you going into MMA (OR boxing).
That's just what I think. I really think boxing is so unique to other martial arts in that it's less about learning several moves and more about execution of those few moves, polishing only 4 punches (sometimes 3) to a high luster and figuring, building a clever solid structure around it (subtle movement and angles), it becomes so illusive that people who haven't done it can't tell what's going on so the reasons for its effectiveness stays hidden, even right there out in the open, even during slo-motion replay from several angles.
Anyways, do what you feel like, in your own timeframe and sequence. Think it out, don't get antsy or feel pressured by others. Too many people are tempted by the ethereal promises of glory floating around their head, glory from false pre-conceptions they have picked up from media and various ignorant half-informed sources. Study it out, go with your gut, think out the cleverest/most optimal way for YOU, and do it your way. Good luck!
Just to be clear, I do boxing and have even uploaded some sparring videos of my boxing gym on here, so not bashing on boxing, that being said...
If he trains boxing to the point he becomes as good as you're saying. He's gonna still have to spend a long time training in grappling, years, to be competitive if he wants to join mma afterwards. Guys like McGregor don't just train takedown defense, they work on offensive grappling of their own. Just like in boxing, no one just learns bobbing and weaving without learning how to throw a punch, understanding how punches and combos work, will help you understand how to better defend them, same applies to grappling.
You'd be surprised to see how many of MMA's touted strikers, actually have a grappling background to them.
Boxing doesn't translate that well in MMA in my opinion, unless you're a swarmer or slugger. If your style of boxing is the traditional boxer, you're gonna get a lot technical boxing shut down in MMA due to kicking, knees, and clinching.
As a slugger or swarmer though, or a smaller shorter fighter who is forced to fight on the inside most of the time, boxing will help immensely. In MMA I think boxing works best for the slugger type of boxer.
Of course what I said isn't definitive but it seems to follow the general rule from my observations.
Taller rangier fighters in MMA will try to keep you at bay with their longest weapons, jabs and kicks. If you're an out boxer you'd be good enough to still fight him from the outside if he was just boxing too, the issue is he is throwing kicks and then timing knees when you come in.
As a slugger/swarmer, past a certain point the kicks won't be an issue. But knees and elbows can still throw you off your game. It depends who you're fighting really. Styles make fights, but in MMA boxing is a whole lot less effective.
Guys like the Diaz Bros, Fedor (back then in his prime), Frankie Edgar, BJ Penn, etc all benefited from their boxing.