I think it really depends on the nature of your antenna. If it is either a well balanced antenna connecting to the coax via a proper balun, or an unbalanced antenna with a good grounding system at its base, then the screen of the coax should be at ground potential and the presence of a ground wire next to it should not be a problem. Poorly balanced antennae and unbalanced antennae without good ground systems can put a lot of RF back down the coax screen and that could couple to your ground wire with unpredictable results.
Martin (G8FXC)