Yes, police officers can check license plates at any time for any reason because your license plate is in public view* This means running your plate is not, by itself, an illegal search or seizure under the Fourth Amendment.
In simpler words: It is not an invasion of privacy. Police officers, like anyone else, are allowed access to public information.
If a police officer wants to make a traffic stop, however, they will need reasonable suspicion of a violation. In this case, the officer is able to scan your plates to check for any existing warrants or suspensions on your record and use them to pull you over.