When a cop runs your license plate they can indeed tell if you have insurance on your vehicle or not.
Just like when you go into the DMV to register or renew your vehicle tags the computer system will tell them whether you're insured or not and who with.
So yes the police can enter your vehicles license plate number and see if your vehicle is insured or not.
If you don't have insurance then you might get a ticket or have your vehicle towed and impounded.