Your comment makes me think of playing catch. Do we really calculate parabolas in our brain when choosing how to catch a ball?
I've never played baseball, but lots of basketball and soccer, and I get this "virtual trajectory of ball" overlay, so that I can adjust my body position, jump at the right time if needed.
Also often you look at ball, memorize where it will fall, then run to get there without looking at the ball. It can take seconds if it's a long ball in soccer, so it can't possibly be just adjusting to the sight picture.