I wouldn't use one in a Wal Mart lot for many reasons (safety, lack of audacity to name a few) and I wouldn't imagine most managers will let you. I would however like to be a fly on the wall when you ask said manager if you can deploy your Tail Veil in the parking lot. That would require you to say that it is basically a tent. Shortly after I suspect you would get your answer.
I do like those contraptions though. Always wantded one when we used to tent camp. That hooked up to say a 1970 VW Van would be sweet!
Good luck!