Yes, I think so from many points of view.

Back in school, I think both a professor and a TA (both psychotherapists) told us it's important that a therapist has hope for each client and also conveys that hope to the client (well, not necessarily in words, but still ...).

I also feel like not having hope for one or more clients might be a factor in therapist burnout. To me at least, that sounds like pointless work. On the part of the therapist because they could see clients they actually feel can be helped instead or do something else that will lead to some results. On the client's part ... well I think a client's reactions can vary depending on the issue at hand, but personally, while I wouldn't go asking a therapist "do you have hope for me??" if I felt that they didn't have hope and trust that I can change certain things about myself and that I can improve myself and live my life well, when, then I wouldn't see that person as a therapist. I wouldn't believe they could be effective and I just need someone who trusts me and the therapy process. So ... to me, this hope equals trust, really.