Can a drone travel beyond the range of its remote control signal?
If the controlling software allows it then yes. There's at least one drone available where autonomous flight is possible; the Vision 2 FAQ says that the drone will continue its "mission" even if you lose the signal to it, although the overall length of the flight path is limited to 5km and the drone will not fly close to airports. Other drones stop and hover or land if they lose the connection to the controller.

Whether doing this is actually a good idea (or legal in whichever jurisdiction you want to operate in) or not is a whole other question.