Incorrect. Warrants have to be specific. An arrest warrant is not a general search warrant (in fact, general search warrants aren't legal). You don't lose your rights because a cop is arresting you.

Now, what can happen (and probably would happen) is the cops can take a drug sniffing dog to the car when it goes to impound and while the owner isn't there and claim "Oh, the dog signaled on the car so we searched it".