If a trumpeter or saxophonist, for example, learned to play music by ear and not by sheet music or formal training, is it more likely that s/he learned the standard fingering names or the concert pitch? (I.e. an alto saxophonist would, from the start, call the fundamental/native-key an Eb and not C).
My guess is that most of these players play with concert pitch instruments such as a jazz band and would just learn the name of the actual pitches their playing. Why bother transposing in your head if you're never looking at sheet music and are always given the key in concert pitch?
But then what do they do when they switch (if ever?) to another instrument in the same family (alto to tenor sax, for example). Do they know memorize both notes for the same fingering, like a recorder player?