We stayed at a couple of Flying J's over the years where we had to make time since we were still primarily traveling with our kids. If I recall both had RV parking available which was away from the truckers parking area. I see no reason why you couldn't run your generator, it's your rig use it as you wish, and at a truck stop it's not like anyone cares. Not that you have too since there is absolutely nothing wrong with your plan, you could check RvParky.com or their phone app for more hospitable overnight parking arrangements in the area. Happy traveling and have a great time in SC!!!