ADVERTISEMENT
If you dress but do not participate at any point in the game then that game doesn't count against your participation limit. Taking the field on any play counts.
So, yes, if you never punt, AND never fake a punt with your punter on the field, and you achieve that feat 12 times in a 16 game season (because, if you are that dominant....) then your punter wouldn't burn a year of eligibility.
The closest anyone has ever come was Kurt Milne for Hawaii in 2006 (5 games with no punts)