Just wait until day one, seems a little pretentious otherwise. No one wants to look like the guy who’s just rushing to update his CV on LinkedIn to show everyone how great his job prospects are.
I had a summer associate for this year from one of my summer firms try to add me on linkedin. He had added the firm to his profile, and the first thought I gave is “who is this guy,” then, “he must be weird.”
The professional norm is to wait. I guess it could help you by making you look overeager to work at the firm when the office hiring manager looks you up online. It could also hurt when an attorney from your firm looking to add other attorneys from your firm stumbles upon your profile and thinks “that guy is weird.” If I was your classmate I would also think you were weird/antisocial. My bet is no one will see, but if someone does see it, 50/50 they think you are a weird.
To your law school classmates it will look like bragging. To people at the firm it will make you seem strangely over-eager. To everyone else in the world, it will make you seem like a weirdo who puts a planned future job on your resume.