If living in the same house didn't make him happy, what makes him think that "dating" you is going to make him any happier.
I think he has to see that first before anything else. That the problems go beyond you. He has to face his own unhappiness first.
How do you feel about the date? Do you want to go? If not, then I would suggest against it since both of you wouldn't be in the right frame of mind. Maybe give it a cooling off period, and then date.
I just feel that he's doing it to settle things in his own head to make him believe that "hey I did everything I could". I don't know where the WASs get these ideas from, but going out on a token date isn't going to make them happier. They have to "want" it to work first before going out. Even if it's a little desire for things to work out. If they don't have the initial desire or feel like they're "forced" to do it, it's not going to turn out very well.
M-43 W-40 2D - 9 and 5
Emotion, yet peace. Ignorance, yet knowledge. Passion, yet serenity. Chaos, yet harmony. Death, yet a new life.