Top Law Schools

I got a new internship and wanted to include it on my resume, I haven't been waitlisted anywhere though so would sending in an updated resume do anything for me?

Some schools ask for updates like this, others don't really make it seem like they want them. I'd contact each school (or look it up on their website). I sent in an update like that last cycle and had it mentioned in a later phone conversation (as a positive), so if the school welcomes updates, go for it.