Yes, insurance will pay but you will end up with a black mark on the policy as you were unable to identify the other vehicle. Whether it will result in any kind of insurance surcharge varies by state.
By law you typically have to call the police to the scene if there is more than $1000 in damage and file a full report within 24 hours (again this varies by state). The police would have checked your vehicle for the initial impact damage looking for paint etc to collaborate your story.
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