This has a lot to do with where you are located like colotrout said. A couple of friends back in the UK have done this with mixed results. Apart from local permits and other regulatory stuff, the quality of water and year-round flow rates are important. Up here in the North East, the little brook than runs past my property almost dries up in the summer and that would be disaster for trout even at 20ft deep.
If you have good alkaline soil and a good constant water flow you can get very good results and natural insect life will flourish. The need for supplemental feeding with pellets etc. will depend on how many fish per acre etc.
The problem comes when stocking the pond since there will be an occaision when fish will escape into the wild and that could start a downward spiral in the viability of the wild fish population if your escapees actually breed. It doen't matter how careful you are, at somepoint it happens (major flood etc.).
When sight fishing, look over your shoulder from time to time, you never know who's behind you