I agree with everything everyone above said. But If you are curious about it and want to see some pond(s) with your own eyes, you can PM me and come by my pond. I too have 10+ acres and a 1 acre pond that is set up different than what you want,but it might at least give you and idea what your place would look like with a 1 acre hole on it.

Mine is managed and we have a mother in law with a non managed/natural pond you can look at that is about 1/3 acre and a cousin that has about 1/2 acre pond that is also un-managed, all within a mile of each other. Just a thought.

As an example on #of fish produced. In 2014 I have taken 45# of CC and 70 CNBG at a total weight of approx.28# and one tilapia about a 1/2 pound. 73# of fish X 60% meat yeild (I agree with esshup) would have me at 44# of meat. We only have 2 bags of quarts right now. I have caught a few bass but they are not really managed because I have a slot only to help manage CNBG my primary focus.

I aerate and feed but cull selectively for my goals. As you stated with a "Natural" pond not only would you be at the mercy of mother nature and living in East TX, as I do, the wide fluctuation in water level could cause you some "natural issues" with any fish you stock. As an example my mother-in-law natural pond has years where no fish are caught and 1 out of three years when we do catch mostly bream and warmouth and it dies off again for a year or two. Of course when the pond completely dries up which is often since 2006 there have been no fish at times.The bird bring in the eggs (I assume) and the cycle starts again at the mercy of mother nature.
I think F&C is right too in that you will need to build your pond for netting because I struggle to catch them as well. Only caught one this year by accident. I have them for algae control and supplemental forage species.

All that said, it is a interesting idea and a challenge I would think, for constant fish yield with a natural small pond. I would add that many of the experts here who manage many ponds would might recommend if you want a more constant fish yield, you might get it with a larger pond of say 3 to 5 acre where a variety of fish could be stocked and allow a balance in a pond with a lot more acre feet of water,bla,bla ,bla.IMHO

Life is more fun with a pole in your hand.