Back to the origonal question, yes. I've never been on a trip, that was more than 3 days long, that I did not supplement my food in some way shape or form. In some parts of the US, at the right time of year, you could easily go for a week, covering ~100 miles "living off the land". If you were willing to be flexible about times and routes, and were familiar with the flora and fauna of the range you were in, you could do this by bringing little or no food at all, I'd bring some.
You would want to take on such a trip utilizing both a fishing pole and a rifle. It could be done with neither, like UL backpacking, knowledge and skill can replace gear. I learned how to tickle trout about 20 years ago in YNP, and have eaten many a fish without ever wetting a line. Same for those "stupid" grouse, I've taken my share by never firing a shot, it is NOT easy, and they are not dumb. these kinds of skills are allot like starting fire with a bow drill, nice to know how to do it, but a mini Bic is sure hard to beat.
Bows, darts, slingsgots, etc. Sure these are all viable, but do require more skill, and time to hone that skill. I hunt grouse almost exclusivly with a bow, if I really had to put them in the pot, I'd choose a shotgun. I've taken dozens of pigeons with a blow gun, and I'm sure you could take allot of small game with one. I never was very good with a sling shot, but know a guy that regularly takes grouse with one.
These meals need not be dishes made up of a singular form of protein either. On a trip to the Uintas a few years ago, another fellow and my self, rounded up more fish and mushrooms than 7 people could eat, for 3 out of 9 dinners. I've had salmon and grouse, slow cooked in piles of wild peas and onions. Dandilion and nettle greens salad, berries of all sorts, cattail roots (always a treat in slick rock country), Pine and willow tea, the list goes on.
I feel that the real debate about doing such things comes down to the question of when and where, wether it is ecologicaly sustainable, and fits the wilderness ethic of the locale.