I had to look up what a Tail Viel is, found it
here.I don't do parking lot, over nighting, but this much I do know, when doing an overnight in parking lots, the goal is to be as unnoticed as possible. Slides in campers stay in, lawn chairs and BBQ's stay put up, awnings are not extracted, you don't unhitch, and jacks are never down.
To set up the Tail Veil would probably draw a lot of attention. I suppose it would be at the call of the store you are using if they would let you do that, or ask you to move on, or just ignore you.
I would think your personal security would be a concern. I know RV's are not the most "bullet proof" vehicles on the road, but they do have a door that can be locked. If the tail gate of your van or SUV is open, and you are sleeping in the back ... I ... well ... I wouldn't be sleeping at all! You're much safer in a campground.
Best you can do, if personal security is not a factor to you, is to call the store, or when you arrive, go inside and talk to the manager and see what that say.
Personally, over my life time, I've seen hundreds of RV's overnighting at WallMart. But I've never seen anyone in a tent.