SWEET! Wonder how this state would evolve to the present?
Hard to say without looking at some two hundred years of butterflies.
The big issues in the immediate period are going to be a) Argentine support for other Latin American independence movements, b) the French Revolution making Spain focus on Europe, and c) the sociopolitical effects of having three versions of revolutionary nationalist republicanism coming into existence at the same time, in the US, Argentina, and France.*
Towards
A), because of the multicultural/multi-ethnic makeup of this Argentina, you're likely going to see not only support for independence, or at least revolutionary, movements in the Spanish New World colonies, but also in Brazil, and possibly even across the Atlantic in Kongo-Angola; which would certainly be highly interesting, in the Chinese sense. Chile at least is going to be lost, and Upper Peru will likely either join the United Provinces, assuming it remains a stable polity, or become an allied sister republic. What IOTL constituents Paraguay and the South and Southeast regions of Brazil are likely also going to see revolutionary activity, which in the latter's case due to size and population concentrations might either split Brazil between a royalist north and republican south, or take the whole region away into independence. The rest of South America outside of the La Plata basin will be out of the revolutionary/republican Argentinians reach, at least for now. Coastal regions of Guinea and the Caribbean might see activity though, especially if the Argentinians, who remember have already freed and given citizenship to their blacks, support the Haitians - that alone could have serious repercussions, especially if the Haitians are more successful, and more moderate.
Towards
B), even without an ATL Napoleon Spain could still be screwed.
iirc the French did invade Spain repeatedly during the revolutionary period, and again,
iirc, there were calls from many corners in Paris for France to either annex Catalonia or make it one of France's satelite republics. One of this is going to happen ITTL with Spain already looking weaker after Argentina goes republican and starts to encourage revolutionary activity in the other American colonies. If so than Spain won't be able to provide any troops or material to the Hapsburg holdings in Italy, and that means that even with British support all of Naples as opposed to just everything north of Calabria falls to revolutionary armies. That's going to have some very large implications for Italian nationalism and the outcome of the war. This also means that only Sardinia and Sicily remain outside of revolutionary republican control, and even then both of them are going to be the sight of some very intense battles between French & Italian revolutionaries both on the islands and trying to cross over from the mainland and the British & Spanish.
Finally, in regards to
C), both the US and France experimented with several different governmental forms, the French more so than the US, who largely retained the idea of a parliamentary republic. IOTL the Argentinians first used a
Junta, which then meant a federation of municipal administrators, generally elected by the local populace, with a Supreme Junta united in the capitol. These Juntas served as a collective executive, legislative, and judiciary all in one body, and employed a directorial system with several people jointly serving. If the retain this system instead of quickly changing to first a triumvirate, and then finally a presidential republic as in IOTL, this will have massive consequences. Obviously such a system is completely alien to note only the absolutism of the Spanish monarchy or the parliamentarian constitutionalism of the British, but also stands quite at odds with American style presidential republics, or the French directory, which still had a separation of powers, let alone the French consulate (which might never exist ITTL). Its open to debate whether or not such a, quote-unquote, "totalitarian," federalist, governmental structure could prove to be efficient or stable, or whether or not it would survive long, but its mere existence as a form of government as opposed to an organizational tool of a revolutionary movement would have quite an impact on republican political thought, which is going to have a serious impact on how the rest of the Atlantic and Latin American Revolutions play out.
EDIT: In regards to
C), this might make the US Anglophobic if the (Democratic-)Republicans have another, major, republican state to point to besides France to counter the Federalists calls for close ties to the empire. That would have huge consequences for Britain, and for North America in general.
* Actually, eight even IOTL if you count the Haitians, Swiss, Dutch, Irish, Corsicans, and Poles - but most people usually don't, for various reasons.