I would hold off on updating them because you certainly can't list it as an actually publication yet. If you have already told them (in the primary or secondary) about the submission, then to update them now only shows that it got rejected somewhere. If you haven't yet told them about the submission, I think it would be appropriate to update them when:
a) you submit it
b) the journal asks for revisions and a resubmission to the same journal (tell schools that your paper is currently "in revision" at whatever journal)
c) it gets accepted for realsies
You don't have to (and probably shouldn't) update for each step, it mostly depends on your timeframe for the paper.
Good luck!