Yes a cop or police officer can indeed see and tell if your drivers license is current or suspended when they run your license plate.
That is if the car you're driving is yours and in your name.
But if you're driving someone else's car and your license is suspended the cop won't be able to tell whether your license is suspended or revoked until they actually make the stop and demand your drivers license.
When a cop runs the license plate the owner of the cars name, address, and drivers license comes up on their computer.
They can also see if you have insurance on the vehicle or not and if you do not have insurance on the vehicle they can pull you over and possibly tow the vehicle.
If your drivers license is suspended then the cop will arrest you and take you to jail for the breaking of the law of driving with a suspended drivers license and then the car will also be towed.