I do not think that this is how I would word this question. I do not think that the Great Depression had an impact on Hoovervilles. Instead, I would say that the Great Depression caused the Hoovervilles to come into existence.
The Hoovervilles only sprang up because of the Depression. As people lost their jobs and homes, many of them starting moving into these shanty town. They named them Hoovervilles as a way of trying to show that they blamed Pres. Hoover for their problems.
So, I would say that the Depression caused Hoovervilles, rather than saying it had any impact on them.