Sure it does, if they have greater capacity controls on the restricted F ticket. You still have the case where lowest J is less than lowest F. And their algorithms could very easily zero out A inventory once P inventory goes, which would ensure the fare hierarchy (i.e., First > Biz).
OTOH, AA recently was offering F fares on JFK-LHR that were less than the lowest available J fare over New Year's. Just over $2k r/t, very tempting. (Biz was maybe $200-300 more r/t).