I've kept chickens and turkey together successfully. The turks can tend to be bullies since they are quite a bit bigger than the chickens, but it didn't lead to issues since my birds had lots of space to get away from each other. They even shared the same coop (not just roosting, the chickens and turkey would all lay their eggs and hatch their babies together in there).
As for the disease thing, blackhead is the biggest concern for turkey. And if you have it, you have it. It lives in the soil and the chickens can carry it and give it to the turks ( though the chickens are not often bothered by it, they would be capable of spreading it to separated poults, for example). Call your local Ag extension and ask if there have been any reported cases. If the answer is no, then all should be well.