I think it could conceivably be possible to do an interesting time travel story that "ties off" the Temporal Cold War arc without putting obscure continuity from Enterprise front and center. I wouldn't chase it down, but I'd be open to it, in the right hands. But the Discovery team would do what it has done every other time it has made a reference to some other part of continuity. We would get a messy, ugly story that casts aside grounded character work for fanwankery that isn't remotely consistent with what came before, which climaxes badly before moving on to some other new hotness. The TCW arc, which was always bad, would end up being made somehow worse by these writers. So I voted "no, just no."
The Temporal Hot Mess should remain on the ash heap of extraordinarily bad story ideas, where it belongs.
I would rather watch Star Trek - The wrath of dried paint followed by Star Trek The search for the paint brush
If Culber's essence somehow still magically exists in the mushroom realm, then there's a chance that Mirror Lorca is still around, too. Kor
I think it would be nice, so that viewers could watch Enterpries, then Discovery, and it would all connect, and make sense, and tell a story in order, that leads into TOS.
Name drop the Suliban and leave it at that, if it must be referenced at all. Preferably in a list of alien species—no need for five minute info-dump or anything.
At this point, I absolutely expect this show to do a detour to the Temporal Cold War to show us how the Borg manipulated the Romulans to go to war with the Dominion, coincidentally at the same time Sisko tried to convince them as well. It will end with the crew of the Discovery needing to travel back to 2018 and having to work together with Khan to transport three humpback whales back to the future. One of Worfs ancestors will have a guest appereance. After that, Starfleet will classify their entire journey, to explain why Kirk didn't knew any of this.
No TCW, they will f*** it up, just like Enterprise did. So no. Other time travel? YES! Why not. It's a part of Trek history and I'd be happy to see it on Discovery.
If they're going to do a time travel episode and they like to re-visit ideas from old series, plus they like to be 'dark and gritty...and sometimes a little fanservice/wanky, I would love to see an episode where Discovery travels to the future, post-Nemesis, but an alternate future created by them missing from the timeline. So Yesterday's Enterprise, but told from the perspective of the time displaced ship rather than the alternate timeline ship. "History has no record of the Discovery after _____," which leads to a dark timeline, where whatever evil Federation starship they encounter in the future isn't a ship of morals caught in a bad situation, but rather the force that is attempting to prevent them from returning to the past to preserve their own timeline, bad and all. They could even throw in "Temporal Prime Directive" or give it a "General Order" number as a reason why they have to commandeer Discovery and prevent them from polluting their alternate timeline. So basically...the Mirror Universe Arc condensed into a single episode, where they're not pretending to be Terrans and just trying to escape...but in the FUUUUTUUUURE. All just a big excuse to bring in Fleet Admiral Janeway as the big-bad and to see some Discovery versions of 24th+ Century Starships. Fanwanky and derivative? Yes. Fun and kickass? Strong maybe!