If I were in charge of an admissions office (and I'm not) I would hold your application until the committee letter arrived unless you were otherwise a superstar (gpa >3.9, MCAT> 37). So, there might not be any advantage to doing what you propose over just sending the committee letter.
If your school is not well known, the adcom may not even know that there is a committee letter and not expecting one, they may be happy with the individual LORs you offer.