First, I would like to make sure I have my terminology correct. The conductor that runs from the "ground rod" to the circuit-breaker panel is the GEC, correct?

Leviton makes a "Structured Media System" that is contained in a (wall-mounted) metal box. The box has a green screw for grounding. (The box will contain telephone and networking wires.)

Is it permissible to connect a conductor from the green screw to the GEC, using some kind of "tap" connector, in such a way that the GEC is not cut?