Legal Question in Family Law in Georgia

If she has tiebreaker decisionmaking, yes she can.

Unless you have valid concerns about your child leaving the country such as the mother is from another country, her country of origin is not part of the Hague Convention, mother has threatened to leave with the child and not return, mother wants to travel to country on the State Department's warning list, etc., the court could require you to sign. I would speak with a family law attorney.