The 'flapping of butterflies' only in Spain, Portugal and Iberian America would be enormous. The event raised by the OP is so important, should not discuss their possible or probable consequences deterministically.
Beginning with an event which surprisingly, is usually quite understated...
The decision taken by the Portuguese monarch refuge in Brazil of the invasion of Portugal by Napoleon, and from there to govern the Portuguese Empire, was instrumental for the formation of state infrastructure, which then enable the creation of future empire, of which the modern nation-state Brazilian, is its heir; in addition to the start of the state centralization with the corresponding military power to suppress the centrifugal tendencies.
With regard to Spain, it would not come to pass the power vacuum, OTL, nor the Council of Regency. Which arise in reaction to the movement juntista, on behalf of the legitimate monarch, first in Spain and taking advantage of the antecedent, emerge the various American juntas overthrow the constituted colonial authorities. Starting the autonomy / independence movement in America.
There were attempts more or less important both internal and external with British support planned and carried out by members of a small minority influenced by the ideas of encyclopedic French and American examples and French revolutionary rebellion.
It is also clear that among the elite Criolla educated, were the autonomists feelings and that in at least part of it, there was some self-identification proto nationalist as evidenced by the debates about the name to give the people on both sides of the Atlantic during the discussion of the constitution of Cadiz, (the representative of New Spain, he rejected the denomination of Spanish Americans, for the inhabitants of America).
But as evidenced by these same debates a shared feelings of patriotism and a sense of community were present in those same elites even after juntista movement started in Hispanic America.
That said, in a scenario where the legitimacy of the authority and prestige of the monarchy are unquestioned and this retained the means to impose its both political and military authority, it is doubtful that members of the autonomist movement make it to take power as they succeeded in OTL, and from there launch military offensive against loyalist and / or peripheral areas.
Not to forget the strong conservatism of the ruling classes Creole and Peninsular of colonial societies and their fear of social revolution, which remained present even after independence was achieved.
Therefore it is unlikely a quick breakdown of the colonial system Spanish, as the likely sources of both internal as foreign rupturist challenges, as had been shown so far, both lacked sufficient military force as a sufficiently broad base of domestic support as to achieve their independence goals.
Finally, given the tendency of the Spanish monarchy to continue applying its absolutist policies and focused on Europe as well as ongoing and unstoppable expansion of the influence of Liberalism among the local elites, it is likely that requests for reform and changes in the colonial system fundamentally increase in intensity and increase their popular support in all Hispanic America, to those claims.
It is also likely to increase the importance of both material and human resources of Hispanic America to the Spanish crown while the local feelings evolve into autonomists feelings.
That the above situation is possible that a negotiated or if no solution is achieved achieved a violent rupture is likely, at least in the peripheral regions and / or a state of constant instability occurs in a continuous cycle rebellion-repression-revolt, etc.
But this possible evolution of historical processes present in OTL, and accelerated by the invasion of Napoleon, not happen, that evolution would take decades to reach the critical point of OTL.