British protectionism combined with a Germany interested in buying South American grains and livestock? Creates a trade alliance, at the least... one that would create interesting tension during any sort of Anglo-German war, and tension with the US over trade once American exports to the region start becoming significant (since South American exports back to the US would be generally minor).
Earlier British protectionism, of course, would have implications on British politics, to the point that a Great War might not happen in the same way - perhaps 'splendid isolationism' is reinforced? Similarly, a Germany that looks to South America to feed itself and for investment opportunities is going to have somewhat different policies of its own.
Assuming the same sort of Great War, though... there'd be less incentive for Germany to wage a sub war against Britain (though not nil, since there's Anglo-American trade to intercept), and more incentive to try to break the blockade. South American states wouldn't really be able to contribute much on a military level, and might be better off neutral (especially if they're allowed to trade with Germany through Holland); at the least, though, they'd provide an example for the US of British mistreatment of commerce.
I'm not sure a long-term military alliance is plausible - what, exactly, would our South American state gain from such a distant ally? - but trade and friendship seems possible.
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Alternatively...
Napoleonic-style Confederation of Germany as an ally against either Britain or (less quixotically) a resurgent Spain? That's not exactly Imperial Germany, but it might vaguely work.