It’s a cartoon. They weren’t making a nature documentary. They were trying to get across the idea of Woody as a crazy, zany character. I doubt Blanc was asked to accurately mimic an acorn woodpecker, but was asked to help create a memorable character. It’s been documented by multiple sources, including Blanc himself, that he recycled Happy Rabbit’s laugh into Woody Woodpecker’s.
Blanc even sued Lantz for $500,000 because Lantz continued to use Blanc’s laugh in the cartoons after Blanc had signed an exclusive contract with Warner Bros. Lantz prevailed because Blanc never copyrighted his voice, but when Blanc appealed, Lantz settled with him out of court.