Not really. They actually care less about "legal issues" generally - they care about things that indicate you're a fraud or a liar. So if you cheated in college and that's on your record, even if it wasn't a "crime," legally speaking, that will get you in more trouble than if you were arrested for a fight in college. Also, they look into your psychological stability and substance abuse. So MAYBE his twitter will become relevant, but it's really unlikely. You don't get denied to the bar for being a pathetic loser asshole, unfortunately.
The fact, though, that he tried to claim that the character and fitness process will take a year and that's "totally normal because it has been so long since law school" is totally a lie - and sounds to me like he knows he's going to get flagged for some shady stuff (most likely all the allegations w/r/t Cell Therapeutics, etc.). But the time since law school is irrelevant (it's not like all the frauds you commit pre-law school are ignored) and he's lying about that.
I've never experienced someone who makes me want, so bad, to HURT HIS FEELINGS and just be mean to. He's such a gross twerp.