I think you will find that the chickens will do a very efficient job of harvesting nearly every last grain of wheat, if allowed to free-range in the stand of wheat. IMO, you would be better off to harvest the wheat and replant what you need to grow the next year's crop, and keep the chickens OUT. If the grain is kept from birds (domestic or wild), the seed heads would drop to the ground and re-seed like any other grass, but you would not have the control over where it sprouted, giving you thick and thin patches. Also, unless you are planting GMO wheat and using Round-Up to kill the weeds, they can eventually crowd out your wheat, or at the very least, make it more difficult to harvest and clean.
I grew a small plot of wheat in my main garden this past year - just as an experiment. I planted the seed (hard red winter wheat) in late October, IIRC, and it grew wheat grass all winter. I do allow the chickens to free range a bit when the garden is fallow, so they did keep the wheat grass mowed for me. In the spring, after the chickens were confined to their own run, the wheat took off and grew, giving me a decent harvest in July. I'll be planting wheat, barley, naked (or hulless) oats and regular oats for harvest in 2010 - wheat and barley this fall, the oats in the spring.
A few things I learned from this experiment - for home use, it would be more efficient for me to plant the grains in wide rows, with soaker hoses running through each row and paths for me to walk through and weed the grain (weeds going to the chickens or goats). As I garden organically, it was difficult to get into the plot to weed, and using sprinklers to irrigate is wasteful of water. Plant your seed more thickly than you think you'll really need, and cover it with a scattering of straw to keep it from the crows until it is established - I lost a lot of seed to crows and other birds. Don't add more seed in the spring if you see bare patches in your plot - it doesn't mature at the same time as the fall planted wheat, and the yield is very poor in comparison. Make sure that when you plant whole wheat from the feed store, it really is whole WHEAT, not mixed with barley seed! I had to sort every stalk by hand to get wheat for baking and barley for soup (and pure seed for this fall) - on the other hand, I now have organic wheat AND barley seed to plant.

Co-planting carrots with the wheat didn't work - the carrots didn't germinate...not sure if it was the mixed planting or the seed, as I generally did not have a good carrot year. Planting the wheat where the potato patch had been worked out fine - the volunteer potato plants didn't seem to affect the wheat, and I'll have a few more pounds of taters than I would otherwise have had.