You can remaster TNG without messing with anything. EVERYTHING has been shot on film. The matte paintings were filmed, the VFX were filmed, etc... . It "only" needs to be rescanned at higher resolution and recomposited (assuming they actually stored everything, but then again they probably didn't). The very few computer graphics they used in 1987 can be replaced with higher resolution versions, too.
It gets more complicated with DS9 and VOY, as there is way more CGI. All of it would have to be re-rendered. The massive battle scenes, Odo's transformations, etc...
I highly doubt that it's as simple as you make it sound. We know that most of the effects (phasers, torpedoes, transporters, various phenomenon) only exist in 480i...film was never involved. It gets a little murky when dealing with shots of various models. As I mentioned, all of the ILM done shots of the six-footer was done on film, as were most of the other stock shots done with that version. However, I'm not sure about other stuff and the reason I feel this is two-fold. One, my own eyes. Much of the per-episode work they did has a stronger video "look" to it than others. Compare the stock shots of the Klingon BOP from TSFS and TVH they used to the new stuff they did in "Yesterday's Enterprise" for example. The other reason that I suspect that is that from a production standpoint, it makes sense. Starting on video means one less production step, one less generation in production, less time and less money - all things that would have been important to the original production. I'm still looking for a definitive reference that details what was done on film and what was done on video though.