1) If they don't learn to fight like European officers, will they win our independence war? Maybe they do, as all they had to do was to take Montevideo (1814) and then defend the lands of the United Provinces. And we know gaucho tactics were good for a defensive war, as Guemes showed in Salta. But would these be enough to resist continuous Spanish incursions coming from the North (OTL Bolivia)?
The Spanish were defeated by Guemes' Gaucho Montoneras and the Siege of Montevideo did not involve Napoleonic tactics as San Martin learned in Europe. So no big difference, except that you might need more mercenaries after the war, or someone else to teach Pachecho, Mansilla, Paz, Suarez, Lavalle, Dorrego.
2) If they fight like gauchos, would they loose civil wars? After all, learning to fight like Europeans didn't made them win Civil wars... Of course, maybe in this TL they would loose earlier...
Fighting like gauchos means an over-reliance on the cavalry charge and elan, while fighting European style means fighting with actual tactics and thinking.
I'd be more worried about the war with Brazil, should it come, and it probably will at some point post-independence.
Paz could beat the crap out of Quiroga, but he was eventually beaten by his own stupidity. Same goes for Lamadrid and his defeat at Ciudadela. Knowing how to fight a war is useless if you're a moron, or if the other guy has more money.
Then there's the invincible General, Angel Pacheco, another graduate of the San Martin school of war, and of course, Lucio N. Mansilla.
To be fair, this country makes no fucking sense.
The better trained generals won the important battles but lost the war due to money problems (Paz and Lavalle in the 1840s), being caught due to stupidity(Paz at el Tio, Lamadrid at Ciudadela, Videla Castillo at Chacon), dumb luck (Urquiza v Mitre 1861), stubbornness (Rosas and the Anglo-French blockade) more stupidity (Lavalle in 1840).
Cepeda in 1820 makes sense as Rondeau was a moron, same goes for Caseros in 1852 since Pacheco and Mansilla refused to command and Rosas was outnumbered, outgunned and outwitted.
So maybe it doesn't matter that much.
Although there's also the issue of how politics develop without San Martin and the Army of the Andes. What do Pueyrredon and Alvear do?