No access to that via API. There is probably a better alternative:
Subscribe to Application.DocumentOpening and within event handler check one of the following:
Application.IsLoggedIn, to verify user is signed into Autodesk account, when signed in I believe the Revit user name is fixed to that account.
or
Application.Username corresponds to the user via check against Windows account (you would have to have a company policy where Revit username matches Windows account username).
If you find these not to be correct you can cancel the DocumentOpening event to prevent opening.
In such a situation your addin file needs to be protected by file system permissions. If they are working remotely on their own machine that is probably not an option but then most things wouldn't be in that situation.
Have to say I've faced the opposite problem where people are not around and they've left worksets or elements borrowed. Mimicking their username to relinquish is then the only alternative to detaching and remaking the central. They didn't seem to consider this possibility with single sign in.
