If a paper is accepted, should we send in an update right away or wait until the paper is published? For the latter, should I include link, DOI, etc. in the update?
An update when it is published is preferred. If your school(s) allow for multiple updates, I see nothing wrong with letting them know that it's been accepted (especially if it's in a high impact journal).
I would send the update as soon as possible. Interviews are given out on a rolling basis, so the later the update is sent, the less likely that it can make a difference.
Accepted is a major checkpoint. Send update. In the process of: In Preparation > Submitted > In Revision > Accepted > Published, the most significant transition, by far, is moving to formally accepted.