Not completely.If Huey Long restore the USA after his victory, does he restore it as a democracy?
He does restore the elections but his focus tree implies that there is a lot of monitoring. That likely means that candidates need to be approved by the regime and that there are a number of official candidates that get advantaged. In other words, Long gets a say in the election and probably ensures it's favorable to him.
Now, depending on his level of tolerance and how far he is willing to go to keep power, that can mean there is room for an opposition to exist and for the regime to liberalize at a later point. But it's likely a regime highly under the control of the President and Long was kind of a control freak OTL. Potentially with noble ideas, but still a bit of a control freak.