To clarify: were their gridlines on the 11-foot Enterprise model, 1966-69? Painted or physical? Top and/or bottom?
Apparently, the upgraded and illuminated 11' model for "Where No Man Has Gone Before"
didn't have gridlines: (Here's an even closer shot
that would have revealed gridlines had there been any).
The black & white promotional shot of the "regular" model (1966-1969) apparently shows gridlines that have been added by a pencil. But even in the original VFX footage these are hard to notice or may have been swiped off because of handling during the VFX production (I don't believe they moved the model by using the warp engine pylons as handles), here's an interesting shot from "The Doomsday Machine"
: Notice the pencil lines near the starboard stern "skylight" which nevertheless only show up as a fragment (i.e. the pencil lines do not appear to be complete).
In close-up shots of the saucer's starboard underside
you can also see very tiny pencil lines (so much for the "paint job" myth? These pencil lines match the position of the pencil lines seen in the b&w promotional shot), however these are absent from the saucer's forward underside
taken at the same time in the National Air and Space Museum.
As for the 1/350 model kit I feel the gridlines to be vastly exaggerated. At a scale of approx. 1/96 these gridlines were already difficult to detect on the 11-footer and therefore would be extremely hard to be noticable on a model reproduction at a smaller scale - in my humble, biased and personal opinion.