Of course the acceptance is effective as the Randi didn't mention the time frame in which Sagan has to answer the acceptance. Since it was an open offer, the acceptance is effective. The statement is True.
Generally when someone sends an offer, the other party replies quickly if interested. But if the other party takes a day or two or more, it doesn't mean that the person is not interested. It may take time, and if he replies in affirmation, the acceptance remains valid.