No. No accessibility standards require attached headphones. Attached headphones sound likes a very bad idea for unattended equipment, as they would be a risk for vandalism and hard to keep sanitary. Headphones are sometimes used in museum style environments.
402 Closed Functionality
402.1 General. ICT with closed functionality shall be operable without requiring the user to attach or install assistive technology other than personal headsets or other audio couplers, and shall conform to 402.
402.3.1 Private Listening. Where ICT provides private listening, it shall provide a mode of operation for controlling the volume. Where ICT delivers output by an audio transducer typically held up to the ear, a means for effective magnetic wireless coupling to hearing technologies shall be provided.