I don't think any Democrat could have beaten the GOP in 1928, whether Coolidge ran again or the GOP nominee was Hoover. As I recently noted here, "One of the big handicaps the Democrats faced in the 1920's was that they were thought of as the party which brought bad times and the Republicans as the party of prosperity. The panic of 1893 and the ensuing depression happened under Cleveland. There had been a recession in 1913-14 which the Republicans blamed on the Underwood Tariff. The depression of the early 1920's started under Wilson. There was no corresponding disaster associated with Republicans (the downturn following the Panic of 1907 was over well before Election Day 1908). This was a major theme of the Republicans in 1928:--a typical GOP campaign card said "HARD TIMES always come when Democrats try to run the nation--ASK DAD-HE KNOWS!"
https://books.google.com/books?id=iQ5cBAAAQBAJ&pg=PT215"
Anyway, I just don't see FDR, even if healthy, being nominated until Al Smith had his chance in 1928. (I suppose it is possible that a deadlocked convention could have turned to a healthy FDR
in 1924, but he would be sure to lose in November.)
And if somehow FDR does get elected in 1928 and the GOP nominates Hoover in 1932, Hoover's campaign is unlikely to be New Deal-ish. Not that he will advocate laissez-faire, but he will probably say that the Depression was caused by the Democrats' "extravagance" and being anti-business and not increasing the tariff enough. Hoover's "progressivism" has IMO been exaggerated, especially by conservative/libertarian critics in recent years. Yes, he had been a Bull Mooser in 1912, but in 1929 he told William Allen White--who of course had also supported TR in 1912--that "every proposal [in the 1912 Progressive Party platform], viewed in the light of today, was unwise." Robert Mason, *The Republican Party and American Politics from Hoover to Reagan* (Cambridge University Press 2012), p. 23.
http://books.google.com/books?id=GkcL4Hwpi4YC&pg=P