Look what I found here :v, very well.
Basically, how would an Integralist dictatorship rule Brazil? Who would be their core powerbases and political pillars of Integralist power structures? How will they do economics, foreign policy, and stuff. Things like that. And also, how long can it last? The PoD is not important, let's say Vargas did not become president and class tension pikes, giving bigger momentum to later Integralist movement to eventually take over.
The integralists would ban all parties, as they believe on what they called the "organic democracy", they saw parties as artificial creations that were made by the elites to divide the civil society and to control the government. The idea of the "organic democracy" is that every single candidate should be independent and thus this would garantee more neutrality on the elections. Of course based on their ideology that completely rejects liberalism and socialism in general, left wingers and liberals would be fully removed from the political camp.
It can last all the way into the 70s, this Brazil could also ally with Salazarist Portugal (they were really close ideologies, so much that Salazar was a supporter of the integralist party after WWII), and fight on the ultramar war.
The economy will be geared towards agriculture, they were corporativists like in Italy but they didn't believed that industrialization should be pushed since they saw the "life at the camp" as the "ideal" society, however after Salgado leaves the scene some other member can change that and push for industrialization.
The foreign policy would have been extremely anti american and isolationist, the only possibles partners are Portugal and post 1947 francoist spain, however Salgado had a plan for a latim american confederation to oppose the US influence in the area.
Integralism was supported by Mussolini's fascist regime, so you can suppose Italy - thus the Axis - would be likely the greatest external allies. Their main enemy, at the time, was ANL (National Liberating Alliance), a coalition of left-winged forces gathered around the Communist Party, so you can guess the fascist-communist polarisation would take the lead on political terms. They would likely join forces with the Axis on World War Two (for context: Brazil's dictator Getulio Vargas actually sided with the Allies). Supposing the WWII timeline isn't changed, I guess the Integralist regime wouldn't last much longer than 1945, not unlikely after a foreign invasion.
They would not ally with Italy, integralists hated italian fascism, there is a article publishied by Salgado in 1944 when the allied troops took over Rome with him commemorating that the city was taken from Mussolini hands, it was publishied on the book "The revolutionary ideology of Plínio Salgado". Italian fascism is modernist, and also secular while the integralists were hardcore traditionalists and supported a christian state, the integralists also crashed with Brazilian fascists at the time (Brazil had many fascist movements in the 1930s, the most famous was the "Legião Mineira", that even got a minister on Vargas cabinet before WWII, Francisco Campos).
Any margin for the emperor to come back?
Well, the integralist action was a republican movement, taken from their 1936 manifest:
"The government shall kept it's republican, federative and democratical form, just adding some minor modifications based on the corporative system."
HOWEVER,
There was a group allied to the integralists, the Imperial Patrionovista order, they were monarchists and many of the integralists were also part of this group, they wanted the return of the royal family, but the royal family refused to recognize them.
A curious fact is that during the integralist aborted coup in 1938, a member of the brazilian royal family, Dom João of Orleans and Bragança, took part on the coup. He was (in)famous for stealing a white ambulance and trying to crash into the gate of the palace of the catete with the stolen vehicle, just to be shot multiple times by the palace guards, he survived.
If Brazil managed to stay out of the war, there's a good possibility that the United States would act like in the 1964 military coup: pretending not to be involved but secretly financing and training those who were "able to keep the red danger away". So if the regime managed to keep popular and political support (I'm not sure they could), it could last decades.
The integralists absolutely hated the USA, Salgado had the same mentality as Charles Maurras that the "civilized world" began to crumble after the american revolution, since it was the first time that a "bourgeious secular state" rose on earth. He saw the US as a octopous that was slowy corrupting all the latim america to adopt their capitalist views.
"Socialism unilaterally fails, resulting in poverty and death, killing your body. Capitalism on the other hand corrupts your soul and make you a slave to live just to consume and keep the system running." Is one of Salgado Quotes.
Then eventually a democratic movement could arise earlier according to the changing conditions. Brazil passed through two dictatorships over the 20th century and both ended peacefully, it's reasonable to suppose it could happen too in a different timeline.
I really don't think so...
The main reason that both dictatorships failed is that they were estabilished as "provisory" dictatorships, both Getúlio Vargas new state and the military regime, as different they were from each other, wanted to be "transitory" regimes that would result on the restoration of the democracy on a near future.
Integralism however had the mentality that they should be there to stay indefinitively, there would be a massive indocrination in schools for the people to be raised with a integralist mindset, and there would be a constant cult for the ideology and the church. Apart from a massive economical crisis, a coup or a foreign invasion, the integralist Brazil can last indefinitively, and also support the portuguese on africa indefinitively.