“The coach mentioned that he couldn’t officially recruit me because of NCAA standards for track. He encouraged me to apply and send my scores to him, and has been in touch with me through email since my visit. Does this mean anything in terms of applications, or is he just being polite?”
Reading between the lines here, I would suspect the coach is being polite. Unless he told you you will be a contributor to the team and asked you to demonstrate your commitment by applying ED, your track bona fides are unlikely to provide a boost. Doesn’t mean you won’t be accepted - but track is unlikely to help your cause.
You could verify this on your own by comparing your performances in your best events to the times that are competitive on the Williams team and in the NESCAC.