Yes, it is usually best to inform your insurance company as well as future auto insurance providers about this incident.

Since it is not a part of your state driving record or claims history it may not affect your rates that will depend upon your insurance company's rating system. Some companies pull reports other than your driving record, like a comprehensive loss report.

Though the person you backed into has not filed a claim, until the statute of limitations are up in your state there is the possibility that they could and your insurance company should be informed so they would be ready for a claim in case one was placed.