Yes. In fact in retrospect I think it would have been more successful than TNG. The established actors would not have had to prove themselves. It took 3 seasons for TNG to really get going. The downside of a Phase II is the budget aspects. Sure, they had models and standing sets, but in the early 80s that motion control was still very expensive and that's what sank Galactica. Shatner started TJ Hooker around the time Khan came out, and he wasn't about to do two shows at once (although Heather Locklear did, with Dynasty) so that kind of closed the book on it if nothing else.
By the time Trek IV was done, the crew were primed and loaded for a series, though, and Shatner could have ended TJ Hooker to do it, but that's around the time the TNG idea was bubbling up.
A big part of TNG had to do with the electronic compositing system and the direct-editing of negatives rather than conforming prints. These cost-saving measures really allowed the show to proceed and that stuff just wasn't around years earlier.