It might be complicated but you could play as Dutch and the rest of the team could operate in FT skins without anyone else on the team visually seeing it- this applies to skins/voice track only on your own local computer/console. If you're the only one seeing yourself as Dutch it is possible for the game to have minimal narrative from Zues so long as everyone has relatively the same lines to speak and view the same cinematics from their own perspective. Of course if you die as Dutch, evveryone else still sees you as a FT member so in theory, you dying as Dutch should not pose a consequence to the match's narrative.
It would however be more interesting if you , as Dutch, could play in 3rd person view (much like viewing the other members when you've died). I'd rather actually like to see Dutch in the camera rather than in 1st person where you don't see your character.