This is a bit of a mess. If you CTB, it will be a serious trauma for them. Even worse, I think, if you don't tell them. I think you should tell them.
The problem is that they will probably ask you to not do it. They may ask you to promise to not do it, and they may even tell someone so you go to a hospital.
But if I'm honest, I think you should try to recover, if not for you, for them. As far as I know, your illness is not necessarily unrecoverable and you haven't tried to recover with their help, and if they are really so supportive, they may be able to help you.
In any case, I think you should tell them. They are an adult and this is something that it affects them too. They deserve to know so they can make a decision themselves. If they want to try to help you, if they want to break up or if they accept it and want to be with you until you CTB, that's their choice as much as CTB or not is yours.