He knew. Its why he protested and offered to take the girl with him to safety. He knew they were seperating them for some evil shyt. In the end, he had no way to intervene.
This is what I'm saying. He knows Stannis would likely do something desperate when the chips were down. Stannis still had a relatively strong army at that point, and just needed some decent days. There's still nothing completely desperate about the situation, besides food concerns.
Idk. I'm leaning that Davos knows something went down, but iffy on Melisandre's involvement, since she refused to talk to him when she came back. He has a more pressing concern now. I'm sure, had Jon not been murdered, he would've forced the issue on finding out things more. I do know he knows Stannis was defeated and something fatal likely happened to the family he forced with him.