I think this rapport thing is either naturally there pretty early on or isn't.

As for sharing things with a therapist where you just don't have the rapport in a natural way, I don't know. I'm thinking if you are able to see them as just a professional with whom you can talk about issues, and get help with finding your own journey in resolving them, and they do have the matching professional expertise for your issues then it can work.

I don't see it working at all if it's supposed to be like deep attachment and emotional dependence on the therapist with some really intimate and special connection with him/her where you can be totally vulnerable like with no one else to try and open up about your deepest feelings and issues and feel so totally perfectly safe about that. I don't think anymore that therapy has got anything to do with that kind of thing. Even if there is natural rapport.

It's got more to do with utilising the therapist's expertise and techniques in working with your feelings and psychological issues. Since the material is personal, emotional material, this is going to be tricky but it's best if you are not totally unconditionally exposed raw to the therapist. You have to keep a level of control for most of it, even if you have moments where you do open up so much and are raw and all that about it. You have to be able to keep the overall relationship in a container otherwise. And there just has to be a natural distance between you and the therapist with that.

That's just my opinion.