The DRL fuse and/or relay needs to be pulled if you don't want your new HIDs to be on all the time. The DRLs also use a method to lower the voltage to the low beams during DRL mode, which will put your ballasts in danger of premature failure.
Using a relay and harness from the HID supplier will cause your HIDs to get full voltage even during DRL mode. This reduces the danger from low voltage failure.
Early non-LTZ models had the factory fog light wiring in some, so check yours to see if it exists. If so, then all you'll need to do is install the lights and switch, plug in the harness connectors, and have the BCM reflashed to "see" the switch and lights.
If you don't have the harness and still want to use the factory switch, be forewarned that it is a momentary contact switch, not one that turns on when pressed and off when pressed again. I made a schematic and parts list available for another member who wanted to use the factory switch and lights but not the wiring. It involves doing a little bit of wiring, but if you're up to it, it isn't all that difficult.
If you don't want to do something that involved then you're better off getting a "regular" switch and have it turn a relay on and off. The relay will turn the lights on and off.
Your driving lights (aka low beams) can be 5000K for great light output, but you may want to consider using 2400-3000K for your fogs. That would make them yellower and more practical in really bad weather, which is their original purpose. Check with chevyguy8893 (use forum search to find his posts) and he'll even tell you that they work way better than white ones.
The HID harness is optional. If you're capable of wiring in your own relay and fuse system then do it that way. If not, then buy the relay kit. It will ensure that the HIDs get full voltage with little or no voltage loss due to the teeny-tiny wiring GM is using these days.
You can run anything you want through an empty fuse, but if the fuse is truly empty (as in Not Used) then there probably aren't any terminals in the socket, or there's only one. But that's what you'll find out when you pop the cover and investigate.