"What!? You bring food with you when you're trail running or backpacking!? That's not ultralight. I can survive for three days on wild berries and pine needles..."
I'm embarrassed to admit it, but I've actually done this, as I'm sure others have, just for the challenge. Three days was the longest I ever cared to try.
3 days in Northern Michigan, eating just veggies (wild leeks, watercress, burdock root, fiddleheads, morels, cattails, spring beauty) and the occasional fish. A fun experience, but not conducive to high mileage days. I'm sure I wasn't meeting caloric requirements either, but interestingly did not feel hungry due to frequent snacking and the fullness factor.
3 days in subzero weather with no food. The ice augur and rod negated any benefit in terms of weight savings. 3 straight days of fish cured me of any desire to try this type of adventure ever again. It was so cold that any fish I caught froze instantly, but stored well thereafter.
In the end, backpacking is just a hobby for most of us, so there's no reason personal preference shouldn't be as good an answer as any. My preference, for convenience and enjoyment is to bring a small cooking system. My stove setup weighs as little as 1.5- 2.5 oz, and (as Dave C mentioned) I can save significant weight by bringing only dehydrated foods. One day's food for me is usually about 16-18 oz, with an average caloric density of 160 cal/oz. This would be hard to match with an uncooked diet. I can't stand energy bars, and would have to eat almost exclusively nuts and nut butter to get close. But even more importantly, there is nothing I enjoy more than a nice hot meal at the end of a long day of backpacking.
Minimalist cooking system I picked up from fastpacker Matt Kirk's blog. Not all runners eat uncooked food. 1.5 oz for the pot, and <0.5 oz per meal for fuel. I think the advantage of dehydrated food offsets the weight of this system. Most of the time though, for convenience, I just bring a 0.5 oz alky stove.
Whatever you decide, I hope you enjoy it. That's what it's all about.