Republican morale would be held until they realize that the UK and France still won't help them. Germany will still be an anti-Communist authoritarian country with lots of sympathy for Franco. In fact, it's entirely possible that with Hitler gone, that UK, France, and Germany are able to reconcile most of their differences and completely screw over the Republicans just as much as what happened in our timeline.
The Nationalists were already in very good position by September 1938. Nothing in this scenario is going to change the dynamic in the war. The Republicans will still have practically destroyed their army at the Battle of the Ebro, and Republican territory is still split in two.
As long as Franco knows that he can win the war if no one else interferes - and I believe this to be the case - then the war more or less still unfolds as it did in our timeline. If real pressure is brought to bear, including Germany and Italy rescinding their support (which I do not see happening), then he may agree to some sort of negotiated peace. I think its past that point.