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Since grades only come out in May, I know this would only apply to waitlisted applicants. Would they request to see your grades when comparing the waitlisted applicants? Or is that part of the assessment already complete?

If it varies by school I pretty much only care about Harvard and maybe Columbia for this information.

My guess is that final semester grades are unlikely to make much of a difference unless you failed a class. You're not going to find much data on this.
If you're waitlisted it's probably worth sending a letter of continuing interest that mentions your graduation honors, though, as well as anything notable you've done in the mean time (internship, publication, whatever).