What protocol does a TDD/TTY use to communicate with a cell phone's headset jack?
TTY/TDD uses tones in the audio band (similar but not compatible with the old Hayes modems) to communicate over telephone lines.  The original protocol uses Baudot code at 45.5 or 50 baud.  In 1994 the ITU  approved a newer V.18 standard.

So I would presume the headset jack would just pass these tones back and forth to a TTY/TDD modem.  It would not be a hidden RS-232 interface -- i.e. the cellphone is not acting as the modem.