most of my flocks always had at least a few game hens, they did ok. they were sorta bossy and were usually on the top of the pecking order when in a mixed flock. the oriental games were much nicer and calmer to me compared to games of other class. the american games i had in the past were alert, bossy, and extremely flighty. they were a nervous wreck but not as much as leghorns. with that said i still recommend getting them but there are other broody non game options too. maybe if you're into american games but not the aggression then you can probably get some longtail breeds, many resembles games and supposedly they are also good mothers.
some of them will probably be ok but different breeders have different stories. most of mine were fierce, independent and bossy. i wouldn't say extremely aggressive but they did stand their ground