Good question. I think it partly depends on how you present the issue to your therapist.
I was doubly embarrassed -- one for having spent so much money on binges and two for spending it on psychics, which I know conjures up images of Miss Cleo for most people. I made it sound as if I spent a lot of money on something I knew was "dumb."
I could feel in my therapist's response that she believes psychics are fake and like she thinks I'm "better" than that -- and I felt a twinge of judgment from that. The truth is that I'm more on the fence about psychic ability than I made it sound to her. If I had presented it as something I wholeheartedly believed in, then I think she would have respected that.
More importantly, we looked at reasons why I binge and worked on tolerating and accepting uncertainty rather than trying to find it with psychics when it cannot be found. Having confidence that no matter what happens with a situation, I am still enough and I will be OK.
I do think it's important to disclose psychic addiction or dependency to your therapist if it is interfering with your life.