Any turkeys can catch disease, not just young ones. So can chickens.
If blackhead is an issue in your area (ask your local agricultural extension), all ages are at risk. But otherwise, chickens and turkeys have shared space since turkeys were domesticated. They have different habits, different preferences, and generally ignore each other. If you start poults and chicks together at hatch, they may become good friends, but the chicks take advantage of the relationship...hopping on the poults as a stepping stone to the outside world, sneaking in underneath to snatch food in the feeder, and so on. But a sleeping, snuggling pile of chicks and poults is cute.
As adults, the behavior is quite the same. The turkeys may roost with the chickens, but they know they are different. They won't hesitate to fly to safety in a tree or rooftop, leaving the chickens on the ground. The turkeys don't even care if a red-tailed hawk is perched nearby, while the chickens panic and run for cover. The hawks haven't messed with the adult turkeys, though they don't hesitate to make a dive at a chicken.