Usually, the answer is no. Health insurance companies do not have a right of reimbursement under Georgia law. The only way a health insurer subject to Georgia state law has a valid right of reimbursement is if, and only if, the insurance company can show that the injured person has been “made whole” or “completely compensated.” As you might imagine, this is usually very easy to defeat, as money can never make a person whole.
However, do note that there are some plans, known as self-funded ERISA plans, that are governed by federal law. If you have one of these plans, then the federal law will trump our state law, and the federally governed plans do have a right of reimbursement. This is why it is important to determine which plan you have and to make sure you only reimburse a plan that has a valid right of reimbursement.