No - that is not what an LOA is. An LOA from USNA is a Letter of Assurance. It states you will receive an Appointment if you successfully complete the remaining items listed on the checklist included in an LOA. LOAs are rare and hard to come by (though I think they are more common than USNA admits but officially they are quite rare). USMA has what I believe is called a Letter of Encouragement which means your application has been viewed as very favorable, but it is not an LOA. Pretty sure LOA for USAFA is the same as an LOA to USNA in terms of definition.
Just because you are 3Q with a nomination does not guarantee an appointment. I think statistically at USNA the odds were still about 50/50 or 60/40 that being fully qualified would lead to an Appointment for USNA 20/20.
The majority of Appointments won't be generated until the February - April timeframe.
There are examples (though few) of candidates with LOA's not receiving a Nomination.
My DD was one of the lucky ones to get an LOA last Sept/Oct, but she did not get her appointment until February.
Is there a particular reason you think an LOA is forthcoming?