All things that has a tonal impact influence my playing, and IMO the board has a big tonal impact. (relatively-speaking)
As for the board's color or inlays affecting my playing?; No not at all.
I only look at the side-marker dots. Looking at the board itself always resulted in hanging my head over in bad posture. About 12 years ago I intentionally started buying guitars with blank boards (no inlays). It didn't take long to adapt, and overall it's been a big help to my already kranked neck and to my comfort level when switching between different models.