Yes when a cop runs your license plate through their computer to check to see if the license plate is actually current and belongs to the vehicle the cop can see whether you have current insurance on that vehicle.
So if you drive without insurance and the cop runs your license plate even if your license plate is not expired then the cop can then pull you over.
You can then either get your vehicle towed or have a ticket issued to you for no insurance on the vehicle.
The cop can also tell whether or not your drivers license is current or suspended or revoked and if your license is suspended, revoked etc then you can be arrested for no drivers license.
Running your car down the road without insurance is not recommended as it can really cost you a lot more than just having insurance in the first place.