I don't believe it would have altered the outcome of the war. Any country in South America would have been isolated from Germany and Japan by the combined efforts of the US and British navies. It would have been extremely hard for them to have any effect on the European or Pacific theaters of war. The only benefit to the Axis would be if their ally could have threatened North America and diverted US resources to blunt that threat. The best ally in that situation would have been Mexico. With such a threat on our southern border, it definitely would have turned the US's attentions to protect against any incursions and not reinforcing the European theater. It would have delayed Operation Torch in North Africa and the resulting Mediterranian and Italian campaigns. All in all, the landings in France in 1944 would have also been delayed resulting in a Red Europe with the Soviet Union overrunning Germany and Western Europe. Therefore, the biggest winner of a South American-Axis agreement would most likely have been the Soviet Union.
That will make Sloniksp happy...
He could hang the "Hammer & Sickle" from the Arc de Triomphe.