If Nazi Germany had survived for a few more months than it did, would America have also used the Atomic Bomb on them?

Well, this is speculative. No way to know. But if we indulge in some speculation, knowing what factors went into the use of the bomb and how the top people in the US thought about it, I think the answer is "no" if we are just extending the timeline a bit but not changing any of the circumstances on the ground. Why? No good targets to use it against (major cities all more or less destroyed), and no good reason to use it (no plausible narrative about how this would lead to surrender). With Japan, a lot of things fell in place that made using the bomb on a city seem extremely appealing; with Germany, even a slightly more prolonged war wouldn't change those circumstances too much, if you are only prolonging it on the "back end." Obviously this requires some imagination as to how it would be prolonged, but I am just imagining we slow down the final invasion of Berlin a bit.

A more interesting situation to consider, in my mind, is, "what if the atomic bomb was ready a few months earlier than it was?", rather than extending the war. That makes it a more complicated situation, because if we are talking about the period at or before the Battle of the Bulge, suddenly an atomic bomb looks like it actually could be useful. And, in fact, FDR did ask General Groves about the possibility in December 1944. Groves said no, because the bombs weren't ready, and he didn't want to drop it from a British bomber (there were no B-29s in the European theater). The logistics would have been non-trivial, but not impossible.

If we imagine the entire Manhattan Project got started earlier, then I think the chances of using a nuclear weapon in Europe start getting quite high. And this requires doing less imaginative acrobatics than prolonging the war — the date they got the bomb was fixed pretty strongly by the date they decided to really build one (as opposed to just do some exploratory research), and there were not any particular "good reasons" for the date being end of 1942/early 1943. The timeline of the bomb development is more or less:

Fall 1939, the US starts looking into whether fission is something to worry about, but isn't making a bomb or really investing heavily in it. (Uranium Committee)
Summer of 1941, the British convince several key American scientists that a bomb is feasible. They take over the program and start to accelerate certain aspects of the research, including developing pilot experiments for the main plants to make a bomb. (S-1 Committee)
December 1942, a request is made to bring in the US Army Corps of Engineers to handle the construction and coordination necessary to actually build an atomic bomb. (Manhattan Project)

Leading to them having the fissile material (fuel) for three atomic bombs in late July 1945, a little over two and a half years after really starting trying to make the bomb.

There's nothing too historically special about 1941 being the point at which the US gets excited about it. One could imagine that the scientists who got excited about it in the UK could have been in the US instead (indeed, they were German Jewish refugees anyway) and somehow been successful at convincing people. Or, alternatively, the head of the US program in 1940 could not have taken their report and filed it in a safe rather than passing it around. There are many arbitrary "delays" in the US program to build the bomb, and if they hadn't existed, the bomb could have been ready months earlier than it actually was.

All of which to say is that's the area where I think we can imagine more historical flexibility, without having to imagine up elaborate reasons why the Germans would be holding out for several more months despite the Americans and Soviets being at Berlin's door.

As it was, the timing of everything meant that they were thinking primarily about Japan as a target from even very early on, and by the time they started doing actual planning for target use, they knew that Germany was just not going to be around that much longer.