I see where you're coming from.
I personally view Woo Joo as a chance of happiness for him.
I stated in a comment before that he seems to be very emotionally hurt, he has issues with his father and seems to get emotionally attached to his patients (maybe that's why he is still deeply affected by the loss of his patient from 8 years ago). He tries a lot to help his patients, putting his own struggles aside (he doesn't seem to have any other interests or hobbies. In the recent episode where he had his patients removed from him, he was struggling to stop doing research and stop checking up on his precious patients). This makes me believe that he is trying to keep his sadness and struggles to himself (At the end of the most recent episode Woo Joo was trying to talk to him about what was upsetting him but he refused to talk about it, resulting in her getting explosive later on aha). I think Woo Joo's anger will also push him into expressing what's on his mind, I doubt that with her explosive personality, she would allow him to be struggling after how much he has helped her (trying to help her with her condition, and finding her a job which she can use her explosive personality in, whilst also using her acting talent).
Woo Joo has the same condition that his dead patient had. This gives him the chance to face his past, which will probably also lead to him being more open about his struggles and sadness. This drama also has a romance tag, so i'm guessing they're telling us that they will eventually fall in love?
I think that losing his patient will make him not want to give up on Woo Joo, he will definitely try and avoid it. And as I stated before, she will probably become someone important to him later on in the drama.
So in conclusion I don't think the ending will be tragic, instead I think our two main leads will heal each others past wounds and they will grow closer together, eventually forming a romantic relationship, :)
\\ This is just my theory though //