you got that right... but every round starts standing. the guys with better stand up will always have an advantage until the lesser striker gets the fight to the ground.
this is irrelevant but i will talk about my wrestling..
i was great in neutral (standing up), i probably got taken down 4 times my whole senior year, and 3 were against the kid who placed 1st in states (NJ -- pretty good wrestling state) and 2nd the year before, i faced him twice that year. i was also great on bottom. i could escape against anyone, and often times would off the whistle hit a stand up and escape in a matter of seconds. this would put me back in neutral and i could get another takedown. top was my weakest, although i was still good at it. however, you don't need to be good at it as you can just let the person up and take them down again. being good at top is just extra, and it can come in handy if u need to turn someone for backpoints or get a pin to win, but if you are good enough standing and on bottom, that scenario wont pop up often.
for conor, he just needs to have great stand up, which he does.. and then he needs to have either amazing take down defense or he needs to become great off his back. he really does not need to work his top game in jiu jitsu. its great to know things so he can take advantage of being on top whenever he finds himself in that position. however, if he just gets so good off of his back and keeps improving his stand up so no one stands a chance against him, he can dominate without a strong top game.
i suggest conor start every practice on his back against great jitsu guys and wrestlers.
i suggest conor start every sparring / rolling session on his back, or in less advantageous positions, against great wrestlers and jitsu guys. work his position, tire himself out, and then keep working it. learn to be able to get up under the most difficult circumstances. he probably is already working his jitsu and knows that's what he needs to improve.... but i am just saying it here anyway.
if he could do that he could be unstoppable and back up all the trash talk he wants