In NYC some of the trolley lines used a trough between the rails for the power rather than overhead wire, it was in some places in NYC and the Bronx I believe.
I have never run across powered traction systems where they only put power on the third rail when a train is present, while it is possible, you could have where when a train is getting near the end of one power 'block' it turns the next one on, but I have never read about it anywhere, at least in this area. With the Subway system they don't even cut power when crews are working on the third rail (unless they changed that recently), because NYC transit operates 24/7, when they need to work on the power rail they do so with it live, because trains are running (the guys who worked on power maintainance were proud of that, friend of mine in grad school was a senior EE with the TA, said those guys were certifiably proud (and crazy.
Basically as others have pointed out third rails have cover boards over them, but doesn't matter on grades, at crossovers and such, they never have the rail unpowered. I don't know if it is true, but someone told me a while ago that MTA and the LIRR never power down the third rail even overnight when they aren't running trains, according to this person (how he 'knew' this I don't know), because they are afraid that if they turn it off weaker parts of the track circuit may oxidize and fail to power up again. I don't know if the cause is true, but I am pretty certain they don't shut it off overnight even though no trains are running.
I have heard stories about foolish young men who would jump off a tree or a bridge at the height of catenary, and hang from the overhead catenary wires back in the early days of transit, showing bravado, and then would drop down from the wire to the ground, swinging out to land on the relative soft embankment rather than the rails. I don't know if that was a cautionary tale or really happpened (knowing how stupid many young guys tend to be, I can believe it). Kind of like the idiots diving off the Brooklyn Bridge, makes you wonder.