Well Long never planned on "running" for President in 1936. IIRC he planned to challenge FDR at the convention and then the American Union Party would form from his faction of the party with another candidate. Burton K. Wheeler, William Borah, and Floyd Olson were considered for the role of sacrificial lamb candidates. Charles Coughlin, Francis Townsend, Huey Long and Gerald Smith were going to use their own bases of support to fracture the Democratic party and lead Alf Landon to victory. 4 years later Huey Long was going to win the Presidency on the American Union Party line.
This is why some conspiracy theorists have speculated that FDR feared that Long could have been a spoiler and was behind his assassination. It's nonsense of course and I honestly don't even buy the premise. A third party like that could have taken a significant number of votes away from FDR and even cost him a few states but I don't think it would be enough to allow Landon to win. There's no way in hell any Republican was winning that election, Republicans were about as reviled nationally as they would be during Watergate or the 2008 financial collapse and the New Deal was so popular that it effectively neutralized any threat that a third party could have posed.
To answer the original question, it's possible but unlikely. They may have come close though.
Yeah....Roosevelt was popular enough in 1936 to survive a third party challenge from the left. New Hampshire was the only close state...that doesn’t get Landon elected. Only a few more states were within single digits.
