Yes 6th chord's can and are mostly seen as sub's or mistaken inversions. Like the Cmaj6 chord is the same as an Am7 chord. For me, the thing that sets these two apart is the tonality. If it's minor it will be Am7, or if I happen to play a C root in a minor sounding key, Am7/C. If it's major it will only be a Cmaj6 (I or IV). I guess you can say I go by the context on which the chord is played, to me more musically correct.

Minor 6th's (ii) can be a sub for the viio chord in the same way the major 6 is. I agree griphon is right it can also sub for the V7 chord, but better in my opinion in second inversion rather than root. See if I got this right griphon, take an A minor 6th chord (A C E F#). Now D7/A which is A, D, A, C, F#. Pretty close to the same chord but what I think connects them better is the interval C to F# (dim5 or aug4) which is characteristic to the sound of both chords.