In principal we were defending "democracy", but in reality we were just containing the spread of communism, which put our government in political bed with some pretty horrible leaders around the world. We were criticized in Europe and of course the Soviet Union for this as a hypocritical country that talked a good game when it came to democracy, but did not follow through in its foreign policy.
As for influencing Brown vs. Board of Education, there are some who believe the justices on the Supreme Court may have been influenced by the views of America around the world and the need to make a pro-civil rights statement, but the evidence on that score is pretty thin, and most of Africa was still a British or French colony in 1954. I'd say there's little connection between the two.