Can you send data usefully over one wire, literally one wire?
Yes it is possible, but only really as a extension to radio if you don't want to consider systems that use a implied second conductor, like the earth.

Radio works, so you can use the single wire to greatly decrease the loss between transmitter and receiver.  With radio propagating thru space, the power per area falls off with the square of the distance to the transmitter.  The falloff with a wire is quite different, with modest distances yielding less loss.  The loss in a wire is exponential due to ever-increasing resistance, so eventually radio actually wins over wire.

You can also have what appears to be a single wire system by implicitly using some nearby large conductor, like the earth, as the other "wire".  Some old commercial power distribution systems worked this way, with the earth carrying the return currents.  If you can send power this way, you can also send information this way.  However, no such power systems are being built new, and I think all the old ones have been phased out and replaced with full out and back wires.