The problem is that even if the Portuguese manage somehow to send a small force from the South to the Incan lands - and even that I think that is unlikely - soon or later the Spanish would be doing the same from the North, and the Portuguese would be "remembered" that they were exploring the wrong side of the Tordesillas Treaty.
True, it is a the low probability event.
But if Aleixo manages to meet the king with a big enough pile of silver its chances go up very fast.
Also the Tordesillas treaty had a little article that stated that if any state manages to conquer any land before it's surveyed it belongs to the part that owns it; this article was included because of the Canaries Islands and later used by the Spanish to keep the Filipinas.
Do you have the sources for this, because the story I knew was a bit different:
I found it on an article about fortifications in Brazil, the author cites some sources.
I don't know if they include the part of the article that covers Alto Peru.
- "De Loreto à Tabatinga - D'une Frontiére l'Autre: Antagonisme Sur l'Amazone au XIX Siécle et Aprés", Jean-Pierre Chaumeil, L'Homme, Vol.32, n.º 122-124, Abril-Dez. 1992.
- "Fortificações Portuguesas no Brasil", Arnaldo Manuel Ferreira, Elo/Círculo das Letras, Lisboa, 2004
- "Homens Invisíveis", Leonencio Nossa, Editora Record, Rio de Janeiro, 2007
It wasn't all the rulers of Alto Peru. It was the governor of the Province of Chiquitos who sent the message asking for Brazilian military support and a probable annexation to the Empire in 1825, after our independence. He sent it to the provisory governor of Mato Grosso (because the one nominated by Pedro I was still going there or hadn't being defined yet, I can't remeber exactly now). But this governor thought it would be a good idea to promote himself as a "man of action", and sent a small force to Chiquitos without asking orders from Rio - he only sent a letter to Pedro I informing the Emperor about the situation and his "quick response".
Ah!
The article stated that some of the Alto Peru rulers asked for military intervention, but didn't explained which ones.
The problem is that Pedro I and the Brazilian Parliament didn't want to upset their neighbouring countries. They already had too much trouble being accepted as the only monarchy in South America, and invade Alto Peru to impose a monarch - and a Lusitanian one - surely wouldn't improve their position. The things got more complicated because Simon Bolivar got the news about the Brazilian invasion, and he - or Sucre, I'm at work now and can't check the details - threatened to invade Brazil if the Brazilian forces didn't retreat from Chiquitos. And to make things worse, due to the serious problems of communication between Mato Grosso and Rio de Janeiro, the Emperor received Bolivar's letter with the threat before the letter of the governor informing the invasion had arrived to the Court.
Pedro I then immeadiatly order the retreat (although the troops had already came back before his letter had arrived) and sent the new governor to replace the provisory one.
Also, we need to remember that Brazil had no condition to fight in Alto Peru. At that same (1825/1828) we failed at keeping Uruguay, a place that we were helding since 1816, where there was a large Portuguese speaking minority, where we had a huge number of troops stationed, and with far easier communication with Brazil than Alto Peru. Also, we lost it in a war with Argentina, a country that had less population than Peru and Alto Peru and that we would actually threat with naval blockades (that would be impossible in landlocked Chiquitos). So, not good perspectives here.
True, pity it looked a good way to get a Pacific coast to Brazil.