I suspect there's nothing set in stone, but part of the pitch for the expensive sets for the finale could tie in to the S31 show. Since it's established that the S31 show will deal with how S31 became the later iteration of that org, it's inevitable that Georgiou returns from the future. Having the Enterprise occasionally tie in might be the best of both worlds.
Another thing to consider is with two shows you are going to need a standard "TOS" setting in which you can pull out for various Starfleet ships. You might see the Enterprise constantly being redressed as a various ships and even bases. Especially since Section 31 still has the issue that "Discovery" had in that you know at some point things have to look like they did on "TOS" and the Enterprise sets are closer to that. Now you also have a bunch of TOS style looking uniforms that you can use, even if they won't matter much on "Discovery." In fact I wonder if Section 31 will fully embrace the Enterprise uniforms of will they keep using the "Discovery" looking ones.
Jason