COVID-19 Outbreak (Update: More than 2.9M cases and 132,313 deaths in US)

Unknown. The study did find an increase in suicides, but not the massive spike people seem to expect.
I would expect that while it was certainly miserable, Americans of the time were unwilling to see each other die of starvation and with so many unemployed, industrial/agricultural accidents declined sharply.

OK I did a little searching. In the first link, the article notes what you said but also states that those relationships have changed from that time to now
https://www.sciencedaily.com/releases/2009/09/090928172530.htm
And this article notes that it was mostly a lack of automobile deaths responsible for the change...since people couldnt afford cars
https://www.sciencedaily.com/releases/2011/03/110324202055.htm