No; that would mess up the revision tracking, because you’d effectively be creating a new revision of the document every time it got replicated to the server. (And then that revision would get replicated back to every client…)
Generally you’d have the client update that timestamp when it modifies a document. It’s usually more useful to know the time at which the document was actually created/updated, rather than the time that it got synced to the server.
—Jens