It's a subtle difference, but I don't think the Set Tour would hold up the same way even the ENT Defiant sets did. The Set Tour's focus is on authenticity, whereas a recreation for filming (like the Defiant) would be more about capturing the vibe. Stuff like more modern choices in materials and finishes, the big screens around the bridge being actual lit monitors and not posters, the way the stage lighting is set up. The same thing, to a much lesser extent, happened with the PIC Enterprise-D bridge, and it probably wouldn't have looked acceptable if it had been an absolutely perfect replica. You can certainly spot seams in TNG-R.
Now, maybe the Set Tour people wouldn't mind having all their exhibits gutted, repainted, filled with metallic details and wired with dozens of actual live computer screens, but I don't know. I really don't think any major, pre-Discovery-style TOS-ification would happen in SNW unless it was something very off-the-wall and conceptual, like cross-cutting between Anson Mount and Paul Wesley on the SNW sets and deep-faked Jeffrey Hunter and William Shatner on the Set Tour sets in the same scene (or even just one long morph or cross-fade, like when that episode of Doctor Who transitioned from actual 1960s footage a modern recreation). Even that, though, wouldn't necessarily involve the New York sets, since if you were visually plugging one show directly into the other, you'd be matching the look of WNMHGB, not the look from the main series.
Now, maybe the Set Tour people wouldn't mind having all their exhibits gutted, repainted, filled with metallic details and wired with dozens of actual live computer screens, but I don't know. I really don't think any major, pre-Discovery-style TOS-ification would happen in SNW unless it was something very off-the-wall and conceptual, like cross-cutting between Anson Mount and Paul Wesley on the SNW sets and deep-faked Jeffrey Hunter and William Shatner on the Set Tour sets in the same scene (or even just one long morph or cross-fade, like when that episode of Doctor Who transitioned from actual 1960s footage a modern recreation). Even that, though, wouldn't necessarily involve the New York sets, since if you were visually plugging one show directly into the other, you'd be matching the look of WNMHGB, not the look from the main series.