Not really. The last nail in the coffin of serious research on the gold standard was "Golden Fetters" by Eichengreen. It has a phenomenal and indisputable country-by-country timeline showing the cycle of deflationary behavior stopping during the Great Depression in country after country shortly following (4-6 months) the effective abandonment of the gold standard. One can argue that N=20 is not significant research, but there is a reason no-one will take you seriously if you do.

I personally haven't met anyone who has argued for the gold standard and has read it although that may be a comment more on the academic backgrounds of the people who used to write pro-gold stuff and stuff it into my inbox back in college than the theoretical basis of the argument. So while gold may have a place as an investment (especially as a hedge against inflation) in large part people who spend considerable breath on extolling its virtues using words like "intrinsic value" and "stability" and "natural" are kooks. Their choice of the word "natural" is also odd since gold coinage is hardly more natural than paper and in fact is less easy to control the asset base.

When economists talk about not repeating the mistakes of the 1930s, they are by and large talking about the importance of maintaining liquidity in the system to prevent deflationary spirals, and avoiding liquidity traps. They are also cognizant of Keynes' proof that Say's Law does not work once people want to start doing things like holding liquid assets, and the dismal performance of things like the zero-inflation policy in Canada and other countries through the 1990s.

I'm amazed by the number of Internet libertarians who have jumped on this bandwagon.