I haven't used T4 in over 2 years, but at that time there was no baggage dropoff allowed for AA flights; might be different for AY, but it is best to take your bags with you to T8 if you don't want lose your luggage.

If LA cannot issue your AY boarding pass in SCL then you will not be able to get it at JFK until 3 or 4 hours before AY flight time (much easier to get them issued from other than the departing airport). Unfortunately the AC outside security is now closed so you probably won't have access.