Generally no, universities can't divulge any personal information without your express permission anyway.
While law firms do conduct background checks, In my experience this kind of thing is usually done on an honour code basis. It's unlikely they would require evidence, but not impossible. If they do request any it does not have to be through your univeristy though, depending on the circumstances you could provide other evidence. Doctors notes, police reports etc.
In my personal opinion, I think the more information and evidence you're able to provide, the more credible it seems.
