Yes, but in most states the cops can't just pull you over at random to look at it.
Here in Texas, it has been done fairly regularly. My stepson, while he was going to college in Austin and driving back to Dallas maybe once a month, was stopped fairly often (usually by unmarked patrol) and asked where he was going and requested for a random drug search.
It was pretty obvious what the "profile" was - he was a college age Asian kid, driving a new black Corvette Z06. They treated him politely, and he had no problems.
I don't like this stuff any better than anybody else - but I generally support the law enforcement people who are just trying to do their jobs.
The real solution is to get serious about securing the border, and setting a real penalty system for illegal employers - in addition to dealing with illegal residents. All have to be done before any immigration reform can be made effective.