It isn't that they supported the Portuguese invasion. They just didn't care beacuse Artigas, the leader of the resistance, was a Federal, and the current Junta* ruling what would later become Argentina (which was more like an idea of a country rather than an actual state at the time) was Unitarian so they didn't support him. And didn't invite him and the other Federalist delegates to the Tucumán Congress... beacuse... well they were Federalists. And we can't have that, oh no.
(it was this kind of pointless infighting that sunk Argentina into barely more than a 19th Century Somalia from 1814 to 1853 or so.)
The obvious solution is that the Tucumán Congress supports Artigas, and gives his delegates a place. This would cause some pretty strange butterflies, probably leading to a diplomatic resolution of the conflicts instead of the endless civil wars and depotism of the following decades. They could repell the Portuguese (not sure how plausible is that, since I'm not an expert on the military of the time) and maintain Uruguay as a province. Uruguayan identity only truly emerged after the Platinean War: they considered themselves as part of the United Provinces before that. And even a while after that, from what I can gather.
Or make Argentina federal from the start, and crush the Unitarians, since any attempt to make an Unitarian Argentina is going to fail as the provinces rebel. Winning the Platinean War is also a possibility, barring British interference.
As for the consequences, well there are now two large port cities obviously. Any acess to the Paraná and thus Paraguay is controlled by *Argentina. The Brazilians coveted the Banda Oriental even from before the independence wars, so they may try to conquer it again: the result will depend on the internal situation of *Argentina and Brazil, and a little military luck (big battles used to define things on this epoch: see Caseros and Pavón on how they can turn the tables quite easily) If they do not suceed on invading or do not try at all (unlikely but not impossible) Montevideo will compete constantly with Buenos Aires on trade, population, culture and above all, customs (which were SRS BIZNESS at the time. There's a reason the fourth article of our constitution deals with that, even before, y'know, rights.) HOWEVER with federal representation, *Uruguay is unlikely to revolt.
You know what, scratch that last part. Civil wars were par the course on this era. Of course some caudillo will start trouble. But MAYBE with a consistent goverment from the start, the country won't dissolve in a dozen squabbling provinces.
Whew! that was long. I don't think I missed anything though, even with my lack of sleep. The Argentine Civil Wars have a number of PODs that could result in very different nation(s). A talented writer SHOULD use those to their advantage, to combat the evil meme of "Nothing Ever Happens in South America"

(this epoch is not my area of expertise though, so I'm not that guy. Please point out any errors/inconsistencies/logical fallacies)
*Not a military junta, on those times. More like a Contiental Congress. But with less union and more douches.