Very much possible. Ardupilot is one of the more full-featured open source packages, but there are simpler autopilots out there as well. It's pretty common practice to at the very least have a GPS based "return to launch" system on long-range FPV craft as a failsafe for the connection to the ground station being dropped.

http://ardupilot.com/

A friend and I are working on this verbatim! Building an iOS interface for controlling the drone in-flight and planning missions, and a little "black box" that will connect to the autopilot computer and send telem data over LTE. We'll post on DIYDrones and FPVLab once it's ready for testers.