At this rate, maybe the American Left will recognize Israel. But I'm not going to bet on it.
Nah. They'll regard it as void because he was under pressure and continue the struggle. If this is genuine, Abbas' name will probably be remembered by the left as the name of a traitor to the struggle of the people (Whittaker Chambers comes to mind). It'll be tough. He has dark skin and he isn't Christian. So he is prima facie, a good guy. But they'll get by that.
The real affront is that this happened during a Republican administration. For that, there is no forgiveness.