Did either of the World Wars involve South or Central America?

Yes, both World War I and World War II involved South and Central America.

WWI

Here is a list of South American countries that severed relations and those that declared war. Sourced from here.

• April 7, 1917 Panama declares war on Germany
• April 13, 1917 Bolivia severs relations with Germany
• October 6, 1917 Peru severs relations with Germany
• October 7, 1917 Uruguay severs relations with Germany
• October 26, 1917 Brazil declares war on Germany
• December 8, 1917 Ecuador severs relations with Germany
• December 10, 1917 Panama declares war on Austria
• April 23, 1918 Guatemala declares war on Germany
• May 8, 1918 Nicaragua declares war on Germany and Austria
• May 23, 1918 Costa Rica declares war on Germany
• July 12, 1918 Haiti declares war on Germany
• July 19, 1918 Honduras declares war on Germany

Although eight other South or Central American countries declared war, only Brazil had direct involvement. Brazil sent surgeons and pilots to Europe. Most pilots served with the RAF, but some served with the French Army. Brazil was mainly involved at sea, however. A good part of their fleet was involved in anti-submarine warfare. However, there we're quite a few delays that hampered the war effort:

“The Italians wanted [the Brazilian fleet] in the Mediterranean, the Americans wanted them to work closely with U.S. forces, and the French wanted to keep them protecting the commercial maritime traffic along the African coast Between Dakar and Gibraltar“. This long hesitation among the Allied command, combined with a delay due to operational problems throughout 1918 that prevented launching the squadron to sea, plus the Spanish flu pandemic that struck the crew at the end of August, meant that the fleet arrived at Gibraltar at beginning of November, 1918, only to see the armistice signed within days, thus putting an end to World War I.

WWII

World War II also saw some South and Central American participation. However, again, Brazil was the only nation of these to send troops to fight.

The members of the Pan American Union, who were all neutral between 1939 and 1941, formed a mutual defense pact at a conference of foreign ministers at Havana, from 21 to 30 July 1940. The "Declaration on Reciprocal Assistance and Cooperation for the Defense of the Nations of the Americas" was part of the Final Act of the Second Meeting of the Ministers of Foreign Affairs of the American Republics at Havana, Cuba, 30 July 1940.

This organization was instrumental in organizing the nations of South and Central America. In fact, before the founding of it, some of these nations recognized Manchukuo as a legitimate state.

Brazil, from 1942, participated in anti-submarine warfare in the South and Central Atlantic and; in July 1944 sent an Expeditionary Force of 25,000 army and air force personnel to the Italian campaign;
-Allies of WW2

During the eight months of the Italian campaign, the Brazilian Expeditionary Force managed to take 20,573 Axis prisoners, consisting of two generals, 892 officers and 19,679 other ranks. During the War, Brazil lost 948 of its own men killed in action across all three services during the Italian campaign.

Argentina was officially neutral, but leaned to the side of the Axis. After the war, many war criminals harbored there.

Chile also was officially neutral, but later joined the Allies

Before 1940, "Costa Rica, El Salvador and the Dominican Republic offered diplomatic recognition of the Japanese puppet state of Manchukuo which was not recognized as a legitimate state by a majority of the world’s nations at the time." Note Dominican Republic is North American.

So, yes, there was involvement from South and Central America, but it did not play an instrumental part in either of the World Wars.