Is it possible to control a drone with a link mediated by the cellular phone network?
Possible: yes

Probable: no

The simple fact is that the cell network is not advantageous for drone control at least not the kind that people prefer. The architecture of the network by nature allows the signal to drop out bandwidth from tower to tower is not guaranteed. This would allow a situation where a drone flying along would get handed off to a tower that has no available bandwidth and the control signal drops out. Dedicated satellite networks allow point to point communication as well as assured bandwidth when its needed.