It would be doubtful that a cop could ever obtain a court order under these circumstances as these conditions fall far short of "probable cause".
I am sure that some rubber stamp judges do would approve though, but that would be a perversion of what a reasonable person would consider probable cause
A better example. Some rookie cop pulls over a guy for a minor traffic violation. Based on a number of minor clues, he (incorrectly) thinks he's got probable cause to search the vehicle for drugs... but he's not quite sure whether it'd hold up in court.
Instead of just going with his gut and conducting what would ultimately be considered an unconstitutional search, the cop lets his partner bring the drug dog over while he's writing out the ticket. The dog smells nothing noteworthy and the rookie lets the guy go without a search.
I'm not agreeing that the number of unreasonable searches would actually decline by any significant amount... but it's possible.