I read this the other day and didn't have a comment at the time, now I'm thinking, Walmart, Costco, Home Depot and the like are not camp grounds and as such you should not camp there.
Most of the places that have stopped us from a short overnight stays in their lots have done so because folks camp there. By that I mean, chairs out, sitting around having a beverage and in general drawing attention to themselves.
Running your generator and AC is pretty noisy and is camping, not just a quick stop for a few hours rest and maybe some shopping and then in a FEW hours, on your way.
So my answer is no you shouldn't do it.