LOAs and principal noms are not really connected.
LOAs are given out by USNA and say that, if the candidate is 3Q'ed and has a nom, he/she is guaranteed an appointment.
Principal noms are given out by SOME MOCs. If the candidate has a principal nom and is 3Q'ed, USNA must give him/her an appointment.
Obviously, if an LOA candidate is also the principal nominee, that person must be given that MOC's appointment (if fully qualified).
However, if the principal nominee does not have an LOA and someone else on the slate has an LOA, and both are fully qualified, both will receive appointments. USNA will need to find another appointment source for the LOA candidate -- probably SecNav (a source to which you cannot apply for noms but to whom appointments can be slotted).