Huey Long would never have been nominated in 1936.
The Big City Machines would never have supported him. Neither would the conservative Democratic delegations from the other Southern States, with the POSSIBLE exception of Alabama and Mississippi.
Consider who controlled the Southern Delegations in 1936:
Virginia - Sen. Harry F. Byrd, Conservative Democrat
Georgia - Gov. Eugene Talmadge, Conservative Democrat
Tennessee - Memphis Boss Ed Crump, Future Dixiecrat
Arkansas - Sen. Joseph Robinson, Sworn enemy of Long
Where would the support for Long come from, outside of Louisiana? Mississippi and Alabama? Maybe. Texas? The Carolinas. The Democratic machines in these states were controlled by conservative elites who were committed to supporting the most sound NORTHERN candidate while holding out one of their own for the VP slot.
From the Civil War forward, aside from Andrew Johnson (who represented the loyalists in TN), there was no Southerner on the National Ticket until 1928, when Al Smith made Robinson the VP candidate to avoid hemmoraging Protestant votes in the South. The only exception to this was Woodrow Wilson, who was Virginia-born, but who was President of Princeton University, and then Governor of New Jersey when nominated. Then, too, the South was not monolithic, and the Southern Establishment viewed Long as an opponent of THEIR interests. It is a fantasy for people to think that Huey Long would have ever been a Democratic nominee for President. If it ever did happen, you can bet that Hiuey Long would have shifted to the right to where he'd look more like Russell Long.