Depends on how busy it is. I have ridden it around. When there is a long line, they clear the cars and make you get off. Regardless - you need a park ticket to board in DTD.
Nominally they clear the trains in Tomorrowland, but I don't think they ever require that guests disembark in Downtown Disney. Most day guests ride it round-trip from Tomorrowland.
We rode in summer (busy) and were made to get off the monorail and line up again for the return trip. We asked to stay and do the return trip but were told we had to disembark and line up again.