First of all, I don't think it's true.
And secondly, even if that's true, mastering English isn't exactly a top priority skill needed for young people to succeed in today's world, especially not up there with math and science (which is ridiculously easy on these standard tests and is weighted less. Actually, does SAT even have a science portion???). SAT does not test general knowledge either. (Yes, I know of SAT-II, but they aren't taken by most people and aren't required by colleges).
No, they're not. Learning them outside of a useful or pleasurable context is almost a complete waste of time, akin to collecting porcelain figurines that you dislike and have no place to store.
If you run into a word you don't know, look it up.