"MCAT scores were weakly to moderately associated with Step 1 scores."
Keep in mind this is for the old MCAT.
How about this one?
http://med-ed-online.net/index.php/meo/article/view/31795
"Multiple linear regression, correlation, and chi-square analyses were performed to determine the relationship between MCAT component and composite scores and USMLE Step 1 and Step 2 CK scores from five graduating classes (2011–2015) at the University of Minnesota Medical School (N=1,065)."
Ahh, much bigger sample size! However, the limitation of a single college still exists.
"These results indicate significant moderately positive relationships between MCAT composite scores and USMLE exam scores."
"Being in the top or bottom scoring range of the MCAT exam was predictive of being in the top or bottom scoring range of the USMLE exams, although the strengths of the associations were weak to moderate."