Yes:
Complimentary In-Flight Amenities
On board, members may receive
Two complimentary drinks, served to the member and/or companion
One complimentary headset, two if with a companion
One complimentary Food-for-Sale item, two if with a companion
Nice! Thanks.
So, considering it says "members may present their AirPass card.." I can't imagine any grounds to turn you down regardless of if flying on Airpass or not, since this is actually unrelated to "Complimentary drink & snack for EXP, CP & CK in AA or US coach" policy and is it's own, published, stand-alone policy (which would explain why it's not listed in the internal policy on this nor in the various wikis on this.)