Of course its possible...

In fact, it is probably a certainty that the US would have recovered fully from the Great Depression even if no government intervention was ever taken. I feel certain that the US has seen and recovered from greater instances of hardship, at least on local and regional levels.

But if you are going to play this game, you can't do it without asking yourself what cost to the society as a whole that course would have demanded. Most of the farms (roughly 65%) in Kansas, Nebraska, Missouri, Colorado and the Dakotas was unusable due to the Dust Bowl-effects that started in 1930 and lasted through 1935. Millions of acres of the most productive soil in North America had turned to dust and blown away across the continent, leaving dry, sandy plots of land that couldn't grow anything but more dust.

There were 300,000 American refugees moving west out of the "dust bowl" to California, hoping to find work and a place to live once life on the farm in Oklahoma became untenable. These "Okies" were housed and fed and eventually put to work under Federal programs, but in your scenario, that doesn't happen. What becomes of these 300,000 Americans with no means to feed themselves and nowhere to live?

Finally, I ask you again (because this has come up before): What is the best guess at how much longer our war effort lasts when, at the outbreak of the war, we don't have the dams, canals, roads, levies, railroads, and power lines that the New Deal programs gave us? Oak Ridge was built by New Deal programs, and we could build it because of TVA and the power it provided. Productions centers like Wichita, Tulsa, Shreveport, Jacksonville all received power needed to build the bombers, rifles, ammunition and boots from hydroelectric facilities that would not have been built without New Deal. The benefits the nation gets from the improvements to infrastructure are immeasurable, in my opinion, but perhaps you feel differently. We didn't do what was done to win a war we didn't know about... but the improvements were good for the nation and the economy, both short term and long term.

Oh, and one more thing... then I'll stop. How many times over have things like Hoover Dam, the Golden Gate, TVA, the expanded electrical power grid, the Mississippi flood control levies, Chicago's South-side Canal, the Huey Long bridge, port improvements at places like Morgan City, LA; Gulfport, MS; San Diego, CA; Tampa, FL; and Galveston, TX paid for themselves since they were built between 1933 and 1939? I know there were silly projects dreamed up during the New Deal, but this is something we always have to watch and monitor when government is spending our tax dollars, depression or otherwise... but the money spent on improvements to our infrastructure are not frivolous expenses, they were and are an investment in the future that is ALWAYS money well spent.

That's my thoughts, anyway.