No, it didn’t help, but the cherished chestnut among the “Free Trade for all!” boosters is that S-H *caused* the Depression.
I maintain that the recent data show that it is now impossible to attribute the worldwide economic collapse of the 30’s to S-H anymore. If anything, protectionism is a result of the collapse of trade, not the other way around, and most people forget that we had trade restricting laws put in place to bolster the prices of ag commodities in the 20’s - long before S-H, we had Fordney-McCumber in 1922. People forget that in the 20’s, ag was fully 30% of the US economy, and that ag commodity prices were declining from about 1925 through to the 30’s, and presaged the collapse in the US economy when the Dust Bowl made its appearance.
Like most of the cherished mythology of the “free trade” movement, the idea that S-H was “responsible” for the Depression will die hard, but I now believe that it will (with a high degree of certainty) die, along with “free trade” as a viable economic policy for the US going forward.
Anyone who studies or follows economics knows that S-H made matters worse, so when you see that argument it comes from someone who doesn't understand the facts, whether it comes from a "free-trader," or a "protectionist" using it as a red herring. (In my experience, the latter is more often the case).