Maybe so if they took turns on it, but I doubt Jack would let Rose back into the freezing water so he could takes turns with it. It looked like it had enough room on the piece of wood Rose was laying on for Jack as well. But I don't think it would have stayed afloat with both of them on it, which is why Jack gave it to Rose so she could survive.
I think he could have. But a LOT of things would have had to play out differently; one thing, Jack and Rose wouldn't have went back to tell Ruth and Cal about the iceberg, this way Jack would not have been arrested and that would have prevented them from losing time and from being in the water for more time then they needed too. Also, if Rose had not have jumped back on to Titanic, this would have prevented Cal chasing them and them being trapped behind the gates and once again; not being in the water for more time then needed. And also if Rose had not jumped back on Titanic, that would have given Jack a chance to find the board, and to no freeze to death. So, yes, if those events had changed/ taken place; then more than likely Jack would have lived.
Um. Wouldn't it just be reasonable to find another piece of debris so Jack could get on too? Everyone always says there was enough room on that door but it wouldn't support them both. Taking turns would result in the door getting soaked so they would still be cold.