Does using a capo change the key or not

Using a capo does NOT change the key on a MD, it changes the MODE and the Tuning. Why? Because, basically, a capo is nothing more than a movable nut/0 fret and the 'missing' notes/frets prevent note/spacing adjustments. On a guitar, or similar chromatic instrument [no missing notes/frets], the capo [movable nut] changes the tuning to one better suited to the desired key and the player adjusts the mode spacing/key scale with fingering. On a MD the modes are 'built in' via the fret spacing, which includes the spacing for a key and fingering doesn't add frets [although 'bending' can sometimes be used as a substitute]. 

The major key on a MD is the identified by the note on fret 3/10. Installing a capo on fret 1 is a mode change [Aeolian] but could also be considered a key change [to a minor key]. The Aeolian mode is the relative minor of the major key and uses the same notes in a different order.

Adding plus frets complicates this, it's like adding another fretboard with different fret spacing.

Bottom line, it is a dis-service to folks trying to understand music theory as it applies to the MD to  perpetuate the myth that capos change the key on any fret other than fret 1.