If college acceptances are your only goal, you might as well stay at your LPS as nothing is guaranteed and you will get a lot of arguments either way about whether boarding school is helpful. If you are looking for a completely different experience than your LPS, a place where you live with your classmates and teachers, where you can fit in sports, arts and academics because of the way they are scheduled, where you will live more independently (but not necessarily with more freedom) than you would at home, then it would be worth considering going to boarding school. The problem with a late application this year is that it would mean you’d be attending a school that you’ve never even visited as it does not look like anyone will be returning to school this year (Cushing definitely won’t be back as Baker has just shut down all MA public and private schools for the remainder of the year).
Take the time to look at course catalogs, special programs, sports and clubs offered in BS and your LPS. Then focus on the ones you’d actually participate in (it’s great to see 100 clubs, but if only a few interest you the other 96 offerings are irrelevant) and see if you would be coming out ahead by going to BS. Maybe what you are really interested in is actually offered at your LPS and not Cushing or Pomfret.
Also, if you applied for 9th grade (and with the very real possibility of fall classes being online), it might be worth your while to at least start in LPS, do a bit more research, cast a wider net next year and reapply as a 10th grader or a repeat 9th.