Ground wire for the most part is for the dispersal of static electricity. After all a direct lightning strike will more than likely give you many more concerns than is your antenna ok.
So absolutley have the ground wire affixed to the coax as this will help in discharging static build up in the coax itself.
Electricity takes the path of least resistance, so if your coax/ground combo comes off the roof at an eave point, I'd recommend 5-6 4-6" decoupling loops on the coax under the eave. Then bring your coax into the house from the loop perpendicular to the house wall. This creates a 90* turn for the static and providing your ground wire contines in a straight path down to the ground will create an easier path for the electricity to follow. Not only have you created a drip loop but you've suggested that the static go somewhere else besides into your house and down to your radios.
Another thing I've learned recently and something I need to address soon is getting the coax off of the roof. The heat from the roof will literally cook you coax. And if it's thundering and raining creates an inviting place for static to build up on your coax. I have seen some commercial "ladders" for roof tops but I don't think I need quite that expense and will probably build a 2X4 ladder using 1X1 "rungs" on the peak of the roof for my coax lines.
