Wild Turkey: A California Native Bird?

I read with great interest this discussion by Don Roberson (titled the same as this post). It was interesting to learn that California Fish & Game were the agents who (re-?)introduced this bird into California (I cannot recall ever seeing one in any of the places we traveled throughout this state during my childhood (to many decades ago to mention).
It seems like they've suddenly become very common in the SF Bay Area in the past 5-10 years. One does not hear about an adverse effect their presence has (contrary to the introduction of European wild boar!!).
In the photo above, my wife and I saw a group of turkeys sneaking through the shade of this Graton apple orchard in Sonoma County. They certainly seem to be very much at home, and easily find whatever food they need to thrive. I suppose that we may discover more on this topic in the years to come.
Meanwhile, would any of our Southern European friends like an American turkey to add to their local fauna?

Attacked by Wild Turkeys in Davis, CA