Not if they were born in the first decade of the period. I was born in 1966, and the first time I used a computer was as a senior in high school in 1984.
I was born in the early sixties and I feel like I have some things more Gen X, and some things more Baby Boomer. I feel I have less in common with older Baby Boomers, whose defining things seem to be the war in Vietnam, anxiety about the possibility of a nuclear war, and Woodstock. My defining things seem to be Watergate, anxiety about the economy (stagflation, high interest rates, unemployment), the Space Race, and the beginning of the tech boom (those happy days when PC meant personal computer, not politically correct).
b. 1963, coding in Basic (punch cards) at age 12, and by age 17 I had about 5 or 6 computers programming mostly in basic and machine code.
The edges tend to blur. For example, Baby Boomers were initially defined as born 1942 - 55. Over the years that got pushed to 1960. The 42 did not change b/c of the clear demarcation line of WWII.
Saying Gen X got 'plopped down in front of a computer screen' is BS. The implication is like we were handed ipads full of games or something to pacify us. Wrong. In the '80s we had to learn how to program it to get it to do anything. Yes, we had a small number of games available on floppy drives (Zork ruled!) but nothing like even a cell phone can do today. And no internet. I bought a book on how to write simulation games that had code and I manually typed it in to get a rudimentary stock market sim, a submarine sim, all text based. It was hardly a time soaking screen babysitter.
Same here, born 1967. I was a senior in HS when I sat in front of a Radio Shack TRS-80 with a cassette tape drive and learned how to program BASIC