A couple things first -
Your chart is highly compressed in and about the years in contest (Great Depression);
This can lead the drawing of the wrong assumptions when considering the legislation/acts of congress (and government in general) year by year.
For instance, the big DIP in GDP bottomed out in 1933 - htis is HARDLY visible on your chart!
Presenting data in this format essentially wipes out one’s ability to perform any meaningful analysis on the going by the fine-grained details of the day ... maybe that’s what the US Dept. of Commerce (souce of your charts?) would like ...
No. Presenting the data in this format (the chart's from Heritage) challenges the assertion that GDP rose in spite of S-H, because it shows that there is an inverse relationship between GDP and the average tariff rate*.
That being said, the assertion I just made can be challenged, but not by returning to the original assertion. The best one can do is argue that there is "no relationship," or "insufficient data."
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*We know that S-H raised the tariff rates on a whole slew of imports (and that U.S. exports plummeted), but we don't know what tariffs were cut in the years following.