Can a minor sign an agreement to pay back barrowed money without a guardian present?

Yes, they can sign whatever they want. The question really is whether the agreement is enforceable. A minor cannot be bound by an agreement however they are usually bound by public policy to return or refund what they have acquired. Usually this is done when the agreement was entered into under fraud (the minor for instance lies and says he is older than 18). If not, a contract with a minor is rarely enforced but it can be enforced depending on the situation.