Does Freuds Theories depend on unprovable claims?

Do you mean "unprovable" or "unproven" claims? 

I ask because that seemingly slight difference affects the entire direction of the discussion.

The ultimate brain killer is the claim god is “unknowable” or “unprovable.” 

To be unknowable is different from unknown. Unknown merely means something not known at present or not known to you. But unknowable or unprovable means that which can never be known or proven. Unknowable or unprovable is that which, by its nature, cannot be known. 

To claim something is "unknowable" or "unprovable," they must explain how they know it is unknowable or unprovable. To do this, they must already know something about the subject: that it is unknowable or unprovable. They have to adduce evidence to support the proposition that it is unknowable or unprovable. The old Burden of Proof rule rears its reasonable head again. 

Does Freuds Theories depend on unprovable claims?

Depends on the theory. In my intro to psychology classes, we go over the many of the greats who paved the way to modern psychology. Freud is one of them. I make it clear to my students that much of Freud's work has been debunked, such as dream interpretation. He has many great contributions such as psychotherapy - talking and listening. He also came up with defense mechanisms , which surprisingly,  have held the test of scientific scrutiny to this day.