When it hit the mat in the first round, Conor came out on top. Now he's not a better grappler than Nate, but the end of the fight says nothing about his grappling. He was already done before he hit mat, and was desperate.
You can push whatever little narrative that makes you feel better though, hahahaha.
He's not a finisher from there or a submission threat, but his grappling is obviously good enough to keep the fight standing, and survive and get some ground and pound with a BJJ black belt like Diaz.