Yes, they most definitely would have used it. Hitler and Japan both were desperate for another win.
There was a reluctance to use nuclear tech to begin with....they weren't exactly sure what was going to happen. They also didn't want everyone to know about it either.
After the two bombs were dropped Everyone knew and capitulated. Wasn't exactly needed to be dropped in the Philippines. (They are expensive)
Also we were running short on fission materials. (More was in the works but breeder reactors only breed so fast)
And we also wanted to start work on fusion bombs. (Orders of magnitude more powerful....also more complicated)