Yes, the Department of Motor Vehicles in most states are notified by insurance companies about the status of auto insurance policies. This is an obligation of the insurance company.
It may not occur in 2 weeks, typically it takes 8-31 days for notification to be processed.
The penalty for driving without insurance varies from state to state. In some states, your vehicle tag can be seized and your car impounded. In addition, some states impose heavy fines for those who drive without auto insurance. Limited sates fine a fee of $150 to $500 for driving without insurance.
CarInsurance.com understands that state complacency allows for states to not uphold the laws of the land. As you will understand from our comments, the states don't consider this offense as a serious offense.
For every dollar you pay in insurance premium a portion goes towards those states that aren't aggressive toward uninsured drivers.
If you need insurance, it is easy to buy at CarInsurance.com.