If it walks like a duck . . . , eh, reb?
I'll give it one shot.
I'd go with the pheasant, because it's an introduced species anyway. But I can tell you the probable result, because other people have done similar things in the past. The pheasant will think it's a chicken, and will stay put, and try to breed with the chickens - you can see some pictures of chicken/pheasant hybrids on feathersite:
http://www.sitelevel.com/click?url=...ngN/BRKRingNHybrids.html&sid=67J2xav8R4EymVuo
(yikes! That's a long link!)
I am not aware of any way to induce broodiness in a hen, other than putting eggs or something similar in a nest and hoping she decides to sit on them. Whether a broody would accept a chick that wasn't hers is not a thing anyone can predict, because every hen is different. Some hens even kill their own chicks as they hatch - though since this bird stole a chick from another hen, she seems unlikely to do that. Hens have raised ducks countless times. I had a duck that was hatched in an incubator but raised with chicks; he took a while to figure out that he wasn't a chicken, but eventually he did.
Realistically, all you will be able to observe in your experiment is what this bird does while it is still in your flock - assuming that the other birds in your flock don't kill it. I assume you feed your birds, so they only have to be passable foragers - that's a far cry from having the skills to find enough food to thrive. I hope you give your birds some type of night time shelter, too - something that would be totally foreign to a wild bird. There have been many attempts to augment depleted game bird stocks with captive raised birds (quail, primarily) that have failed miserably, because the captive raised birds simply hadn't the skills to survive, and couldn't adapt to the lifestyle change quickly enough. I believe that the most likely result of this experiment will be that, if your bird tries to "return to the wild", it won't survive, because life as a chicken won't have equipped it to do so.