It depends on the leader and his wherabouts.
Evo Morales, president of Bolivia lives in La Paz, while the Bolivian government is somewhere else. Sort of same thing in The Netherlands, Amsterdam is the capital, but the government is The Hague.
Let's say the Goverment district is placed there
Indeed, our president lives in La Paz, but two branches of government are also in La Paz. We do have two capitals: La Paz and Sucre. La Paz is the seat of government where both the legislative and executive branches reside. However, the judicial branch remains in our historical capital, Sucre. This was done as a safeguard of sorts to not render a President all powerful in case of a coup d'e etat--we have had our share in the past. It would be cool if there would be an expansion where you could actually do such separation, but I digress.
As for the Inca playing well with the new mechanics, I believe they would fit well, both with Golden and Dark Ages, considering they had both, especially their downfall at the hands of the Spanish. As far as governors are concerned,
@Eagle Pursuit is right. To quote the Ancient History Encyclopedia: "Local administrators collaborated with and reported to over 80 regional-level administrators (a
tokrikoq) who were responsible for such matters as justice, censuses, land redistribution, organizing mobile labour forces, and maintaining the vast network of roads and bridges in their jurisdiction. The regional administrators, who were almost always ethnic Incas, reported to a governor responsible for each quarter of the empire. The four governors reported to the supreme Inca ruler in Cuzco." Part of Bolivia, Peru, Argentina and Chile were part of one of those quarters: Collasuyo. I continue quoting: "To ensure loyalty, the heirs of local rulers were also kept as well-kept prisoners at the Inca capital. The most important political, religious, and military roles within the empire were, then, kept in the hands of the Inca elite, called by the Spanish the
orejones or 'big ears' because they wore large earspools to indicate their status. To better ensure the control of this elite over their subjects, garrisons dotted the empire and entirely new administrative centres were built, notably at Tambo Colorado, Huanuco Pampa and Hatun Xauxa." Loyalty was a big factor, as you can see, or well, maybe forced loyalty in many cases.
So, I think the Inca's fit very well, and even if they didn't I would still rally for them. They are just cool! I hope they do justice by them. Long live the Sapa Inca. I wonder who they will choose to lead them? Pachacuti o Huayna Capac?