What would happen if aforeign power (pretending to be an allied, to add insult to injury)suddenly abolished american constitution a decided that things would work as they consider now? It would lack legitimacy and would be considered a direct agression to american sovereignity and legislative tradition. Well, that's exactly what happened in Spain, trhough the sovereignity was embodied by the figure of the crown and constitution was theset of different fundamental laws and traditions (not too different from common law). Thus, spanish juridical tradition had well shrined he idea that in absence of the monarch, the sovereignity returned to the the people, its actual owner (this is Luis Suárez in the 1500's, I'm not making this out) and thus the people took arms to defend it and formed Juntas to exert it (it was nor the first, nor the last time). Has Napoleon understood this, he probably would had let Joseph living happily in Naples and would have profited of Ferdinand VII's stupidity...but it was easier to think that spaniards were a bunch of obedient sheeple.
Without causing a war of national liberation in a wink of eyes in Spain, the situation for Portugal becomes complicated, thus the possibility of incorporating them to the Continental Blockade (the original goal of the iberian Campaign) increases, though not sure about the consequences of this for Britain.
As Hasdrubal points, it would also free more polish troops, mwith their excellent cavalry, wihich would have and effect in other scenarios. It also butterflies Bailén, and its psychological effects encouraging uprisings in Germany.