Yes, correlate is the right word and my assumption is far from baseless.
"The national correlation between LSAT scores and first-year grades tends to be around +0.4. By comparison, the national correlation between undergraduate and law school grades tends to be around +0.25. The correlation for both variables combined is approximately +0.5." http://www.napla.org/LSAT.htm
Furthermore, I find it ironic that you view 3 hour law school exams as "one of the only factors (besides people skills/personality) [relevant to] legal success" but you blithely reject the predictive value of the LSAT. Why is the act of vomiting onto paper a semester's worth of material clearly so much more predictive of legal success than other factors? However, assuming that law school success = legal success and LSAT success = law school success (as stated above), it follows that LSAT success = legal success. Hence, if you accept your own proposition, you are logically bound to mine.
Finally, I should note that I am not defending the LSAT because it particularly benefited me (I transferred), but because it has demonstrated predictive value, is not hopelessly inflationary (like GPA) and weeds knuckle-draggers out of the profession.