No, because that would alter the document and create a new revision.
Also, it wouldn’t be the actual time the document was updated, just the time that the updated document was received by the server from the client (which could often be minutes or hours later.)
In a distributed system like this, document updates are performed by the client. If you want a server-synchronized timestamp on a document, then you have to have the server do the updating, which brings you back to a traditional client-server system that has to be online to function.
—Jens