Not necessarily. He did the former, which means he "crossed universes" at the points, not at a location where the rails would run parallel but at a distance from each other. And in "Mirror, Mirror", he hopped tracks but not at the points but much farther down the line. For him, it's either-or, not both. Although we don't quite hear Kovich establish that only a close combination of the two tricks would be harmful. Perhaps "Mirror, Mirror" plus all the TOS, TAS and ST4:TVH hijinks put together had already made our Spock a marked man, and he just took his sweet time dying?
The hapless Lieutenant Commander spoken of here would be akin to Mirror Spock swapping places with Prime Spock permanently in "Mirror, Mirror", and in his later life additionally engaging in the 2009 movie hijinks and thus traveling in time in a significant fashion he never has the opportunity to reverse. Although we never hear Kovich say that reversing one's time trip would protect from the grim fate, either. Perhaps our putative Mirror Spock would have been doomed by the back-and-forth time travel in the assorted TAS episodes and ST4:TVH already?
Timo Saloniemi