Not quite, more because Americans have elected a president more than 2 terms, all the more likely here with populist programs, and because there won't be a consistent opposition.
But, okay, I could see it where he still runs things behind the scenes, which would have interesting long term repercussions. But even if he does leave 12 years later, the Long programs will continue. Forever. Share Our Wealth ain't going away, namely because unlike the New Deal, it will be enforced with rather... dirty methods to say the least. The GOP will never recover.
The only reason FDR was elected for three terms was because of the war. And without the War there is no super recovery. The only reason the economy got to the levels it did in the late 40's and 50's was because of Wartime production.