Ah ok. Well, I haven't got any first-hand experience with truly wild American turkeys, but from what I've read, like all wild counterparts of domestic poultry they are somewhat (or in some cases extremely) susceptible to diseases domestic poultry commonly carry (but are resistant to), as they're not exposed to them naturally... Or they're only exposed to weaker wild strains of the diseases which have become quite strong under domestic conditions. So chances are having them regularly associate with your flock is ultimately going to do them no favors.
Turkeys can also become quite aggressive over food or breeding resources like nesting areas, but I'm guessing that if you don't try to restrain them, or have them breed in your coops or nearby areas, you shouldn't have that issue... Probably.
Them feeding on the pellets intended for domestic poultry can be detrimental to their health, they're not adapted to a domestic diet. I'd be concerned about the impact on their wild viability, or that of their offspring, but maybe that's just me. Generally wild birds feeding on processed products intended for domestic poultry or birds does come with problems.
There may be laws or regulations concerning them of which you'd need to be aware, depending on your area, but I don't know for sure about any of that.
Best wishes.