I do not think that Huey Long was destined for the Presidency in 1935. In 1936, there is no way he could have dethroned FDR for the nomination. If he had tried, that effort would simply serve to further marginalize him within the party. And that get's to the central problem, or at least, one of many central problems for a Long Presidency. By 1935 Long and FDR did not have the best of relationships, and that bad relationship made the idea of a Long nomination all but impossible. If Long's split the vote plan had worked, which it probably would not have given the size of FDR's victory in that election, it is hard to imagine the Democrats rewarding Long with the nomination, seeing as he's the one who cost FDR reelection. If Long doesn't make that effort, or rather, if he let's someone else run in 1936 as a plausible deniable surrogate, then the chances of FDR losing in 1936 are even smaller. If FDR is re-elected in 1936, then there's no chance for a Long Presidency. Even if FDR retires, he's going to hand pick his successor, and I doubt he would pick a political rival like Long to succeed him. Also, by 1940 Long's political moment will probably have passed, even without assassination. All in all, Long surviving probably had a greater impact on Baton Rouge than it does on Washington D.C.
Granted, a Long Presidency is not impossible, with the right set of political circumstances, anyone could have been President. But his success is unlikely, and at the time of his death, next to impossible. You probably need something like having FDR die when and why Cermak did. FDR's health probably means that a successful assassination attempt would be instantly fatal, but predicting what happens when FDR dies is easier if he lives for another couple of weeks or so, so that he's inaugurated in the hospital. That way, you avoid a constitutional crisis.
But even if we presume a terrible Garner Presidency, a worse depression, and everything that goes along with that, Huey Long still has a problem to overcome. He's a southerner.
So all in all a Long Presidency is unlikely, and he'd probably be a disaster as President.