I agree that it depends on what type of government they had and what their relationship with their neighbors is like. But since everyone keeps calling them the Cali Inca lets go with the more centralized government.
I think that it’s pretty likely that they’d have a lot of internal issues after the diseases set in. If the central authority is hit hard by the diseases like the Inca were there could be conflict or a loss of cohesion in the Cali Inca which could make fighting off conquistadors very difficult. As you said a depopulated nation won’t be able to easily hold down son much land so once the Spanish heard a rumor or two about gold they’d start moving in. Maybe at first they resist but like we saw with other native peoples guns won’t save them forever unless they can somehow produce them on their own and in large quantity.
Who are these conquistadors? A couple hundred Spaniards (like Pizarro, Cortes, de Soto, etc.) can be overwhelmed with 2-3K native forces no problem. Such forces shouldn't be hard to mobilise for a local governor or what the central emperor might demand if he doesn't want these people in his territory. The Spaniards will be pissing off the locals already by looting them for food and water. And after a few failed expeditions, the Spanish have no reason not to clamp down on outlaws and try and normalise trade and foreign relations. This is especially relevant by the 17th century when the Dutch and English and probably others will be around to trade with the Cali Inca.
This is why I think you need some straight up luck to win in a conquistador expedition. Sadly, history has few examples of major civilisations defeated by conquistadors for us to follow, but I don't think it's unreasonable to say that it required a lot of luck. If we call them the Cali Inca, then hell yes will it require luck.