So wouldn't the Prime time line had ended in the Naked Time episode?
It might depend on how big or significant a change you made. If after the time travel the Enterprise engaged in (in Naked Time) Kirk simply went on to the Enterprise's next destination, and made no effort to communicated with the Enterprise that hadn't yet traveled backwards in time, the impact of that particular time travel would have been zero.
No harm, no foul.
To all the other incidents of time travel in the show, the JJ-verse's old Spock said that there exists some kind of mechanism that would try to repair time lines (I'm not looking up a direct quote on my damned phone), to "correct them."