That map, however, is a bit misleading, since it shows as settled lands which were in fact in Indian hands. Here's a map of the territory that would become OTL Argentina in 1809, with its population numbers:
What I meant with my previous post is this:
While there is a tiny bit of truth in the notion that in 1810 the May revolution was at first Buenos Aires thing, the notion that the rest of the country only recognized it because of the Armies sent North by the Assambly is entire false. Yes, these armies help, but only a bit: many place recognized the Revolution even before the armies from Buenos Aires arrived. And the only reason why the revolution was able to survived was because there was local support for it. The "army" that defended Salta was composed mostly by Salteños. The army that would liberate Chile was recruited mostly in Cuyo.
The question is, even if the british conquer Buenos Aires, would they find support, specially in the interior, not only to conquer the rest of what's now Argentina, but also to defended it from the inevitable Spanish counteratacks, from both Chile and (OTL) Bolivia? Who would give them supplies and men for the advancing British armies? Would the people living in the conservative interior side with them, or would they prefer to side with the more culturaly closed armies from the neighbour Spanish colonies? Where would they find the men need it to conquer Salta and Cuyo, while, at the same time, make sure nobody will rebell in Buenos Aires or Uruguay? Remember they'd also need men to defend the southern border from Amerindian raids.