If a pilot completes an AQP program with a part 121 airline, does completion of all training and passing the line evaluation also qualify as a flight review and instrument proficiency check for continued part 91 operations?
It depends if the AQP qualifies as a pilot proficiency check. Most likely the the outcome will be a pilot proficiency check.
§61.56 Flight review.
(d) A person who has, within the period specified in paragraph (c) of this section, passed any of the following need not accomplish the flight review required by this section:
(1) A pilot proficiency check or practical test conducted by an examiner, an approved pilot check airman, or a U.S. Armed Force, for a pilot certificate, rating, or operating privilege.