Is it possible to allow multiple users to edit a shapefile using the MapWinOCX?
Not really. You could say that the library presumes that it owns the file reference. This is probably true of any shapefile driver. Edits are made in memory and saves would overwrite anything on disk. You would need a sophisticated mechanism (or a central server) to notify any clients whenever a change was made, for example, and to manage concurrency. Now an OGR layer would be different, in which case the database engine might be managing concurrency for you. But you would still require constructs to bring updates into each client and properly concurrent edits.