It’s not the “missed on day” that might be the issue, but rather the nature of the applicant’s involvement in “offensive”/sexual joke that might be a problem.
There have been colleges that have rescinded acceptances based on such things, so it would not be impossible to think that a prep school might also rescind an offer if they become aware of such behavior.
Not knowing the details, neither of us can assess whether it’s an issue or non-issue. It is no longer 2020; final transcripts will be required everywhere.