The farmer next to us rears 10000 pheasants for shoots and pheasants are the most common birds in our garden. They often visit the chicken run to steal food but I've never seen them attempt to mate and in fact the chickens usually just ignore them or chase them away.
I've had around 30 chickens every year in the past 10 and there's never a day goes by without I see several pheasants visit the runs so I reckon if I don't get matings no one will. I think this must be a very rare occurance and to have a chick hatch and survive another rare occurance so I suspect you're looking at something like a 1 in a 1000 year event to get a hatchling by chance.
In the experiment of 1400 inseminations in the link only 3 live hatched so approx 1in 500 matings produced a hatchling (0.2%). Also of the 100 to 200 eggs you get from each hen in a year how many are incubated/ brooded? In my case I rarely hatch more than 15 chx a year from a total egg count of say 20 hens laying 150 eggs each so 3000 eggs. So I hatch 0.5% of my eggs so even if I had a mating and it produced a fertile egg I would only have a 0.5% chance of selecting it for hatching and then only 0.2% will hatch. So to get a good chance of one phicken hatching I'd need to have something like 100000 matings. I've no idea how many matings occur per year and as I've said I've never seen one in 10 years and I keep 30 chx within a few hundred metres of 10000 pheasants. If I assumed 100 (which is on the very high side I would think) that's a 1000years of hatching to produce one phicken by chance.
I guess what I'm saying is the probability of this being a chance hatchling from a stray mating is very remote so I suspect this is unlikely to be a phicken.
Of course probability doesn't quite work like that and it could happen in the next batch I hatch as likely as the 1000 batch I hatch. Why not post a photo and we can all havea speculation!
HF