Will Latin help me improve my English Vocabulary on Standardized Tests?

Probably. I took Latin in high school and I made the 99+ percentile on the SAT. Every Latin word you learn is usually worth 2 or 3 obscure English derivatives. Just the Latin word for red gives you ruby, rubicund, rubicundity, rubric, rubescent, and rubescence. Learning 100 roots and a couple dozen suffixes rapidly multiplies into 1000 words of vocabulary that rarely appear outside the pages of college entrance exams.