I dont think adding pheasant blood would be good for extra kick... maybe just cool colors and appearance. but without fertility it is only a one time deal and no way to improve upon through subsequent breeding back to the gamefowl side.
I don't think it would add the desired zip, and then there is the fact many chicks that do survive to adulthood seem fragile often not living as long as a chicken or a pheasant... according to people who had an accidental mating or actually have fiddled with this. Now I do not know if the cross causes a problem or if it is something else like diet issues.
The math is not in your favor 1000 eggs at 6-7% is 60-70 fertile eggs but a 42% hatch rate would give you 25 to 29 chicks with possible 1% defects that you must cull on top of that but less defects than the other option which gives you 190 to 50 fertile eggs but 78-20 chicks but which results in 12 times the birth defects you will have to cull so that is up to 9-10 chicks further loss.
I have to find the longterm fertility notes... but often one gender is sterile as I pointed out with green jungle fowl cross domestic chicken.
I have often wondered about this idea of mating pheasants to chickens for gameness/ability and I wonder if what is really meant was chickens of pheasant type body like the Sumatra as that makes a heck of more sense. Remember people thought birds like the Sumatra (there are other breeds like the Minohiki or Yokohama with the "pheasant" look) or Green Jungle Fowl, Sri Lankan Jungle Fowl, or Grey Jungle Fowl where pheasants in the olden days. Most people seem to do it either as a Mad Scientist thing or to get interesting new feather patterns.
There is bits and pieces on behaviors as well on these crosses and they make different noises but I would not expect them to be game but who knows. I am no expert I just read up on this a few years ago as I had no idea it could even be done till I saw the first image on the net.
I also have wondered if this might be an old school folk joke, like the chicken version of the Snipe Hunt. Somehow I can see some tough old guys telling the young guys this just to pull a prank.
It is a mighty big list of species that can cross with the chicken btw. I would love to see the Silver Pheasant Cross also I found a Peacock Cross (old black and white photo, very tall bird).
http://www.aviculture-europe.nl/nummers/08e06a07.pdf
The link is a little paper on crosses, but there are science paper too (because college kids need projects
) and if you do a search you can find lots of images and stories about how it happened by accident in someone's flock or someone fooling around with the idea.
I am not telling anyone what to do or not do but understand you have challenges and need patience and the breeding might or might not give you the long term desired results. Crosses often need very special diets or they die young. Long-tail breeders have done a lot of experimenting with the jungle fowl and some folks who have are on BYC they post pictures too.
Peace All.