absolutely, listen to some organ fugues and find that 8 finger tapping thread in advanced techniques.
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Putting technicalities aside (Physical ones, that is), would it be possible to play a contrapuntal harmony on one instrument, such as the guitar or piano?
Ofcourse. Isnt counterpoint just the art of combining two melodies or voices? So wouldnt chords be contrapuctual to a degree?

Anyway, thats mostly how baroque style classical guitar is played.
[U]        | |                     [/U]
[U]        |/     .-.              [/U]
[U]       /|_     `-’       |      [/U]
[U]      //| \      |       |      [/U]
[U]     | \|_ |     |     .-|      [/U]
      *-|-*    (_)     `-’
^ It is important to understand that while Counterpoint implies chordal harmony, chordal harmony does not imply counterpoint. Reason being that for counterpoint to be counterpoint there must be a sense of independent line and there is nothing that necessitates that a chord or a chord progression must poses an independence of any kind.