No it won't kill the ballst if not hooked up. You can connect the green (ground) wire to your system ground on your circuit. Just connect it to the green wire on your supply, assuming the supply is grounded at the outlet.
125 Gal-35 Gal Wet/Dry-Tetra-Tec PF500 HOB
(3) AuquaClear 301 Powerheads-600 GPH
Automatic Tempature Controller
5-6 Inch Sand Bed-200+ lbs of LR