I don't know how well it would go over in the aftermath of the Court Packing Scandal. I would venture the Republicans and Conservatives would blast it as FDR trying to gerrymander more votes out of the system with youth that were inexperienced and had known nothing before Roosevelt so of course they would vote for him.
I could see it maybe happening shortly after WWII with a "these boys just fought in the greatest war we've ever seen and they can't vote for their president" argument.