Of course she should thank him. She needs to have a back bone and not be bullied by the Farrows.
Regardless of current events and politics surrounding Woody Allen, Cate Blanchett does owe him some gratitude. The awards she receives for Blue Jasmine are due to Allen's work and final product.
She can thank the man, but it would be counter-productive to praise him.
The Court record shows Allen had abused Dylan and she needed to be protected from him so he did not get custody of her when he and Mia split beside the fact he became sexually involved with his son's adoptive sister.