At worst I could claim to be an Andy Warhol fan, would that fly?
I've done something similar one time when a minimalist surfing trip took a wrong turn. I learned that if you (a) have a car where the seat goes down flush with the trunk or hatchback (b) have a good sleeping pad (think REI) and warm sheets, then you can get a great night sleep and look pretty inconspicuous from the outside (no one can see in very easily since you're below the window line).
Also, placement within the parking lot is important, not too close, not too far away.
I think you'd have better odds with a tradesman's van/truck for some obscure service. Not a craft meth heads would be magnetically attracted to steal and fence tools like a plumber. Something unappealing like grease trap cleaning service. Or contents you don't want to screw around with, like an exterminator service.
You'll run into some interesting state laws about commercial drivers licenses, and registration of commercial vehicles. Just because you're sleeping in it, doesn't mean according to the cops that its not a commercial delivery vehicle that you've borrowed or whatever (who cares why) and as such both you and the truck should be licensed to actually deliver sodas for hire. Some states have weird laws. You may even be required to have a business license and business insurance to get the commercial vehicle registration.
A magnetic decal sign applied to a plain old van when stopped might be wisest. Can't be pulled over for something you're not displaying and when you're parked, unless you're about to get a parking ticket, no one cares if you're a properly registered commercial vehicle anyway.
Also, on every highway there are rest-stops and trucker rest areas. Some of these have pay-per-use showers and most have a parking lot you can park overnight in and free toilets.
The national/state parks are beautiful and are very welcoming to visitors.
Camping out in Walmart or in the back of strip mall carparks - not such a big deal.
WORD OF WARNING - you are to an extent at the mercy of whichever asshole in a uniform shows up - DO NOT HAVE DRUGS IN YOUR POSESSION. THis can make a "lets roust this johnny-live-frugal out of the neighbourhood" to "cuff him and book him".
My advice if travelling cross country - great to have a sleeper, but also buy a propane stove, some good camping gear, some fold up camp chairs and half a pound of sticky and make the most of the incredible national and state parks. There are many, and they are cheap.