Quite a few D1s will want you on campus that summer taking a class or two and getting acclimated to your new surroundings.
IMO, it's mostly about freshmen making a good first impression when they arrive.
For position players that means showing up in the fall in the best shape of your life. You're still going to have to prove yourself every day, but that at least gets you off on the right foot. If the summer collegiate league is a step up in pitching over your alternatives, then jump right in as long as you can manage the playing schedule while focusing on S&C (most are finished by early August).
For pitchers, you want to manage your summer so that you're coming into fall practice ready to compete at a high level. You do not want to be exhausted from a long summer with too many innings. Again, playing summer collegiate ball could be a good way to face better competition, but not at the risk of overuse.