Depends on the hunter. Here some game wardens have told hunters that any turkeys that have white on them are fair game anytime since they don't want them contaminating the bloodlines.
It happens all the time. The Wild turkeys (bronze) crossing with your Bourbon Red will make Red Bronze poults.
I know people who thought it was neat to have the wild turkeys around so they left treats for them. Eventually they wished they had never encouraged the wild turkeys. The novelty...