Yes, you can still file a claim against the other party's insurance policy.
You may be subject to some consequences since you had no insurance coverage yourself. You might receive a citation from the responding law enforcement agency. You may also have to pay a monetary fine and you may have to show proof that you have obtained an insurance policy.
In addition, your license might be suspended and you may have to satisfy the financial responsibility laws for your state . This means that you will have to buy an 'SR22' insurance policy. An "SR22" is a certificate that establishes proof of insurance and is filed with the Department of Motor Vehicles in your state.
You can get a FREE "SR22" insurance quote here.