True as Aslan was afraid of her wand that's why he only agreed to meet her if she left it behind.Jadis did not fear anything so she agreed and went to Aslans camp with out it and demanded Edmunds life and being Jadis she was not going to leave until she got it. Aslan knew this so he did a deal with her and took Edmunds place but Jadis did not know that Aslan knew a bit more magic than her.If Edmund did not break her wand he and Peter would have been turned to stone and Aslan too as he pounced on her.