Not to discourage new discussion on this topic, but there's several existing threads that also address your question:
https://amp.reddit.com/r/AskHistorians/comments/2uodfp/did_heisenberg_manage_to_develop_the_theory/
TL;DR: Not close
Here's an excerpt from one of /u/restricteddata 's answers:
The very short answer is that the US actually was trying to build a bomb. The Germans were not — they were doing basic research on nuclear reactors. But understanding why the US decided to do this, and the Germans did not, takes some exposition.
One does not bumble into making a bomb. It takes a hard decision, because it takes considerable resources, coordination, policy decisions, etc. The Americans did not commit to building an actual bomb until 1942 — the earlier work (e.g. of the Uranium Committee formed after Einstein's famous letter) was very basic, not coordinated, not about producing a practical result. Then, in 1942, they decided to go full-steam ahead at producing a bomb, and pulled it off after 3 years or so of intense investment and focused work.
The Germans never did this. They decided, in 1940 or 1941 or so, that atomic bombs were not going to be weapons of the present war, that nobody else was going to make them, that they were not worth the investment. It was not that they were so ignorant of the possibilities, but they judged them to be beyond the scope of wartime mid-1940s science and technology.