I don't really talk about my suicide thoughts to my T. Some weeks ago I talked to her about that, because these thoughts were really bothering me. She told me that if I really want to kill myself, I should call her (but that can only during workhours) or my doctor. She also asked if I had plans. If I had, she would have to take some action. So send me to the hospital or some crisis house or whatever.
Your T would probably send you to the hospital when she thinks you're an immediately danger to yourself or others. But I don't know how it works. I think that will depend on the T.

I never have concrete plans. If I'll actually do it, it will probably be an impulse. And I know I won't call anyone. Didn't told her that.