Interest in TOS did not need the JJ movies to retain or build interest. As of this day, what average person ever talks about the JJ films?
I would say that if it weren't for Abrams's films, Star Trek in total
would be completely dead, because it was already pretty much dead not long before them
. So yeah, like it or not, the new movies did help.
The Berman productions died, not the interest or popularity of TOS.
The NG films hit a new low with each new entry, DS9 was what could be best described as a niche interest within ST fandom, while Voyager
(aside from a couple of episodes in E
's final season) force fed all that was ever wrong with Berman's stewardship to the point where it was hardly ST at all.
In comes JJ, and instead of creating all new characters, or trying to piggyback on the Berman shows, the studio went to the face, heart--universally recognized identity of the ST concept: TOS. One can argue--confidently--that the JJ films did not bring attention back to TOS, but the situation was/is reversed.
All one has to ask is: would anyone care about a JJ-Trek film with new or rebooted Berman characters?