No. Trains run on rails by definition. Without the rails, the track pieces are basically just 2×8 plates connected together. I have no reason to believe that the train wheels would line up with the groove that holds the rail, that said groove would hold the wheels in place, or that the ride would be smooth if it somehow did.
I don’t have any 9V track handy or I’d take a look. I checked BL to see if anybody sells just plain metal rails but BL doesn’t list them as a separate item. I’m looking at the BL pic of the 9V track though, and the plastic actually sticks up to hold the metal rail, I still doubt you could run a train on that though.
I also forgot the most important part, you’ll need a train engine. If you end up doing 9V, you’ll need to find a 9V train engine, and that could be the most expensive part. If you end up going RC, I’m pretty sure they’re available on Lego.com, they’ll have a wire coming off of them that connects right to the PF battery boxes. For practical considerations in operating during public hours, I’d strongly recommend 9V, but for reasons of cost and availability, you might find RC preferable.
I hope this works out for you cause this sounds like a pretty cool project. If I dig out some 9V track I’ll take a closer look though, cause I am worried now that Lego didn’t design the metal rails to be removed and there won’t be any way to obtain any to install in the prototypes.