No, not really. Spock's exact words in "BOT" were:The Earth/Romulan war lasts twenty-five years and it was a century ago.
Did it start 125 years and end 100 years ago?
Did it start 100 years ago and end 75 years ago?
Did it start about 113 years ago and end around 88 years ago?
See what I mean? There's room for interpretation.
"...the Neutral Zone [was] established by treaty after the Earth-Romulan conflict a century ago." (italics mine)
Furthermore, he explained that no one had breached the Neutral Zone in the time since the treaty was established. So one must allow for a full century between the end of the war and the time when the Romulans began their incursions in early 2267 (give or take a few years if you presume that Spock was rounding off the time span).
The subclause "a century ago" modifies "the Earth-Romulan conflict", not "established by treaty", so yes, there is room for interpretation. Thank Ghu some writer came up with the "Vulcans speak so precisely they go to two decimal places" tradition by the second season of TOS.

Besides pushing the war to the distant past, we could choose to belittle it. That, too, would be a good way to ensure that it is forgotten except by the fanatical few. And it would make sense that a conflict between the primitive Earthlings of yore, and an opponent those Earthlings could handle, would be a very forgettable one. Perhaps something that ended the very moment the big boys like Vulcans or Andorians stepped in - but still something that meant a lot to Earth specifically.
Not a bad notion, but if I recall correctly, in one of the Dominion War episodes of DS9 someone said the Federation hadn't fought a war on this scale since the Earth-Romulan conflict, implying that it too was a major interstellar war, not a minor skirmish.
Marian