Pretty much, but don't expect the Axis to make as many friends as the Soviets did, fascism does not export well
No, certainly. But I see many nationalist movements who might see fascism as the lesser evil, if only because fascist powers are too far to harm us. IOTL, many nationalist movements denounced both British and American economic "imperialist" policies in Latin America. They expressed their admiration of the Hispanic roots of Latin America, and saw the "Anglo" world as the enemy (and the cause of most of Latin American problems). Some of these movements had some sympaties for fascism, even AFTER WWII (!), as was the case of the leaders of the 1952 Bolivian revolution who nationalized the mines and gave land to the Indians.
So, seen from outside, I don't see such a different scenario than the one of OTL cold world, with the US trying to keep Latin America under they control, and governments here or there occasionaly changing sides and trying to ally with the other band.
Internally, however, within Latin America, things might be very different, as the groups which supported USSR within each Latin American country won't automatically support the Axis, and nor would the groups which IOTL backed the US support them in this scenario. But this doesn't mean that the opposite it's true. Different class and sectorial alliances will be established.
It's hard to say which. Much deppends on what happens to the USSR and communism. Is the USSR still alive? Has communism lost all prestige, or is it still a thriving ideology?