I believe a Captain Sulu series would have worked 15 years ago. I would have certainly watched it, as I was in love with the Excelsior at the time and considered Sulu to be a Captain with mucho gravitas. I think the effect of such a series would have been a positive one, at least for me. I love the movie era Star Trek, it's my favorite. I love the ships, the uniforms, the technology, I love it all, and I would have happily continued on to whatever Trek afterward to see what awaited me.
With VOY, I didn't feel that way. Less than a season into it I started fading. I was still on a TNG high and didn't like the darker feel of DS9 (yet) but didn't like the clinical, bland feel of VOY (still don't). Now, your mileage may vary, but after VOY, I was hesitant to see what was next, because it just seemed, oh, I don't know, foreboding because if VOY had become milquetoast (and for me it was certainly that), what would follow?
So for me, yes a Captain Sulu series would have had a more positive effect. As for the franchise, I believe so as well.