There is a Brazilian novel where this is exactly what happens: An Incan Empire was a Portugueses vassal. The novel is called "Xochiquetzal: an Aztec Princess between the Inca":
http://universofantastico.wordpress.com/2010/01/19/xochiquetzal-uma-princesa-asteca-entre-os-incas/
A short translation:
"Before speaking with the king and queen of Spain, Columbus went to Portugal to propose his plan to get to India by the west. What if he suceeded to convince them? [...] an adventure narrated by an Aztec princess leaded to Lisbon to be educated as a christian and married with a Portuguese noble - Vasco da Gama. [...] in this world a most Fortunated D. Manuel reduced the Inca and Aztec emperors to vassals and the "Three Cabralias", but withouth crushing their culture and society."
Futhermore, there is a "civil war" between Castille and Aragon, a reason of why Portugal could claim the whole American - I mean, Cabralian - continents to itself.
And, to finish, a map by Antonio Luiz Monteiro Coelho da Costa, reporter of the Brazilian magazine Carta Capital:
I've never read the novel, unfortunatly. And there is no version in English, yet. :/