If a shared parenting agreement is terminated, does custody revert back to unmarried mother?

If a couple was never married (nor ever lived together) and they have a child, and they have a shared parenting agreement which is terminated, will the mother be granted sole residential parent and legal custodian? Based on the Revised Code 3109.042 (which provides that an unmarried female that gives birth to a child is the sole residential parent and legal custodian until a court issues an order designating another person as the residential parent and legal custodian). If a shared parenting agreement is terminated will the Revised Code take effect and the unmarried mother gets sole custody, since there is no court order?