I don't think there is anything wrong with asking, but I have two things that I think are relevant to think about. 1) Most T's do not specialize and in fact in some states they are not allowed to say they have particular expertise in x y or z. A specialization is rarely something that is certified or anything other than the T deciding to "specialize," whatever that means. 2) pay attention to how you ask the question, if you ask whether "he wants" to work with you, that's about his feelings about it, as opposed to asking "I would like to work with you long term, is that possible? If your friend was out with you having a meal, would you ask her if she wants to be eating with you? I think you can presume a T wants to work with you if s/he makes an appointment. But perhaps you are more concerned with the long term issue rather than some absolute desire?

Also, even if T does not "specialize" in x or whatever, doesn't mean the person doesn't have the experience to be helpful. I would not presume a "specialist-- which I think is more about marketing than competency" is a better therapist than someone who doesn't "specialize" in that area. Again, I think you can be more precise in your questioning of the person, asking the question you are really after. Rather than ask, "are you competent to help me?" which I don't think would result in any good answers because a T should refer you out if that's the case, so the fact that they are sitting in front of you suggests they think they can help. Instead you can ask, can you tell me a little about your experience working with clients who have X issue?

Again, asking questions is not a problem-- it's a really good thing in therapy. I just think that some questions are not set up to get terribly good answers, and asking more precise ones may get better ones, IME as a person who asks a lot of questions for a living and who has asked T a lot of questions over the years.