"The Americas" means both North America and South (Latin) America. They are 2 continents. "The Americas" does not refer specifically to the USA only. It includes every country in the 2 continents.
NOTE: An "American" can technically mean any person from either continent. A Brazilian could be considered "an American". However, in normal usage - all over the world, I might add - if you say" "I'm (an) American", it's immediately taken to mean that you're from the USA.
Americas might appear as the title of an encyclopedia article. Wikipedia uses it that way here and also cites articles with the same name from The Columbia Gazetteer of the World Online and Encyclopaedia Britannica. But in the article itself, the appears with Americas consistently. So, no, I would not consider it correct to use Americas in place of the Americas.