When including Primary Addressee on the Output tab of a Constituent query, the field is populated on the Results tab, even if field is not actually populated on the Constituent record.
Query is designed as a grouping tool and not a reporting tool.
When including Primary Addressee on the Output tab of a query, the query does not give additional formatting options. It uses the default format of: Use 'Primary Addressee', otherwise use 'Full Name', as is used in Export. Therefore, even if the constituent record does not have a Primary Addressee populated, the constituent's full name will still populate in Primary Addressee column of the query results.