Yes, and probably not as rare as people think.
Probably not as common as you think. Given that only one county in WV actually voted for McGovern, an 18 yr old in '72 would be 62 this year, lifespans in coal country are shorter, and there's been hefty depopulation in the coal counties especially the southern ones.
For example in 1972 McDowell county voted:
Nixon 8972
McGovern 6811
In 2012:
Romney 3959
Obama 2109
Of course, a surviving retired coal miner in Florida could fit the profile, but they'll keep getting scarcer each year that goes by.