So you're stuck reading Twain's The Adventures of Tom Sawyer and Melville's Moby-Dick. You find yourself wondering whether the effort will be worth it: will any of this reading pay off when it's time to take those dreaded SATs? Can reading old books help me develop my SAT vocabulary?
The short answer to this question is: probably. Why? Because many of the words used in those old books are still very much in circulation.
You have two types of lexical libraries in your head. In linguistics, these libraries are called "passive vocabulary" and "active vocabulary." Passive vocabulary is associated with listening and reading; active vocabulary, which is usually smaller, is associated with speaking and writing. Passive vocabulary develops first: as a baby, you spend about a year producing no understandable words, and during that time, your rapidly self-wiring brain is greedily absorbing all the language it hears. Even when you finally start speaking, your passive vocabulary continues to grow. Trying to get your active and passive vocabularies to be about the same level is one of the Great Quests of your life. Many people are voracious readers; this by no means guarantees they'll be competent writers.
This biological reality obtains all throughout high school: your brain is still self-wiring, believe it or not, so everything you cram into it will have some sort of influence. The authors you're reading in English class are master word-slingers; they don't write a lot of "Duhhhh..." and "Uhhhh..." dialogue. Instead, they tend to lace their prose with phrases like "a vexatious situation" and "her surreptitious glance"-- almost as if they knew that, over 150 years later, someone would be needing such vocabulary to score well on the SAT.
The best thing you can do for yourself is to be curious about the words you encounter in your reading. Look up every single word you don't know; don't simply rely on context, because context can be misleading. Make flashcards, write sentences, look the words up on Google to see how they're used by others. Do everything you can to help yourself! Don't act as if your test results are a matter of fate. They aren't. You control your destiny, which means you're responsible for how well you perform on those crucial exams.