This story is not based on an actual incidence that happened. The only bearing it had on real life, according to the author James Hurst, was its symbolic representation of his failed singing career. But there was no real life Doodle. See the sites below for more information about the author and the story.
This is an interesting question and one I would have to say no to. If you check out the links below they will tell you that there is no autobiographical relevance to the story and the author. In an interview Hurst actually told a reviewer that he wrote it as an illustration of his failed singing career. It is also interesting to review the link on the historical context in which the story was written in. It discusses briefly about eugenics, which is selective breeding. It's a good connection that goes with the story, but it is not based on a true story.
No, the story is not real but based on something that could possibly happen.
YES ITS BASED ON A TRUE STORY