The feed isn't the problem, the chickens can eat the higher protein gamebird feed and thrive on it.
The problem will come when your tom comes into his first breeding season and doesn't have his own hen. Can you imagine a large tom breeding a tiny bantam hen? I can, I've seen it- its ugly (and for the poor hen I saw it happen to, resulted in death). There's a good chance your tom and rooster will squabble, over the girls they both think are theirs. Really big birds and really small birds together can be a recipe for disaster. Now, if you get the tom a couple of hens, everyone may get on ok. Or not. They are living beings, so you just won't know until you're there.
Mu turkeys (1 tom, 2 hens) lived with my chickens (standard Cochins) without much issue. The only problem we ever had was our Cochin rooster trying to breed the turkey hens, which would then make the tom mad and usually result in a little tussle between the boys. Turkeys are alot of fun, but you gave to consider the size difference there. Good luck!