That's a good question. But I think the game itself will want to somehow keep the Sims alive, meaning that they will have to cook food, have indoor plumbing, and yes.....bills. (unless you buy the "no bills ever" LTR) As of right now, there are not any options available to have your Sims pee outside or eat plants that they don't prepare in a kitchen. I bet that you could still build a very rugged world, but you'll have still have to have some "outhouse" facilities, and a place to prepare food.
If you're good at modding, you could always make a toilet that looks like a tree stump and they would use that. You could also make kitchen appliances to look like trees or boards. There's a lady over at TSR that makes just that kind of stuff. She made a bunch of it for Sims 2 but I don't think she has yet made any for Sims 3 yet.