Typically the document title would convey which part of the site you were on, e.g.
Dashboard - MyApp - though sometimes apps like Facebook will indicate when you've received a new message using the document title.
For our app, we have queries that take from anywhere between 15 seconds and 2 minutes each. My idea is to indicate something like
Report Running - MyApp, so that a user can switch tabs and work on something else, but still notice when the query has completed. Is this an acceptable feature?
An alternative to this might involve the favicon, similar to how Github indicates when a build test is running using the favicon.