It’s kind of a terrifying question to think about when it comes to one of the most powerful Jedi that’s ever lived, but the fact is that in the Legends canon, Luke Skywalker DID turn to the dark side for a brief time when he attempted to find out what had drawn his father to the dark side. The unfortunate fact is that he ended up being lured to the dark side by a clone of Emperor Palpatine and turned against his companions at that time, becoming Palpatine’s apprentice, much like his father. It took a concentrated effort to bring him back to the light, but the obvious result is that it did happen and Palpatine was destroyed, at least for a while. But trying to think about what might have happened had Luke gone to the dark side in the most recent trilogy isn’t too difficult since it feels as though things would have gone very differently, or at least they should have. It’s still a wonder as to whether or not Luke would have made his way into isolation had he gone over to the dark side.
Then again, it might not be too far-fetched since Palpatine went into seclusion on Exegol, albeit to oversee the culmination of his long years of planning. With Luke, it feels as though his own disappearing act might have led him into seclusion simply to get away and stay away, much as he did in the movies. His avarice and lust for power as a Sith could have seen him lay a trap for any unsuspecting individuals that might be drawn to the planet he’d selected for his isolation. One has to wonder if Leia would have sensed his fall to the dark side, or if she would have been unable to glean anything from Luke. One fun fact about the Sith is that they’re not all the same and that they do have their own methods of serving their own needs.
This is just a theory, but perhaps Luke would have made his way to Ahch-To to lure others to him, to keep the world out but to draw others in. If that had been the case however then it kind of feels as though he would have needed another delivery system for the information that would lead people to him since it’s hard to see R2-D2 putting up with a Sith Lord, though stranger things have happened. More important than his removal to Ahch-To is the moment when would have turned to the dark side, since it feels that cutting down Ben Solo while he slept would have been the moment when Luke’s story diverged. Killing his nephew would have likely broken him, but considering what he’d already been through up to that point, it does feel that he might have been able to step away from the dark side, but he could have fallen just as quickly as well. For the sake of argument, seeing him fall to the dark side would have changed quite a few things since this means that Kylo Ren wouldn’t have become a threat, the Knights of Ren might not have been so poorly used, and it’s not hard to think that Luke and Snoke would have gone head to head eventually.
What is likely is that Snoke, or rather Palpatine, would have found someone else to bend to his will, and would have perhaps found someone weaker or far more powerful. It’s a big galaxy, there are still plenty of people out there. But had Rey still found her way into his orbit somehow, it feels as though he would have been powerful enough to dominate her without fail. If anyone doubts this it’s easy enough to remind them that during The Last Jedi he was able to make her look like a novice until she picked up a lightsaber and decided to ‘finish’ the fight. The reality that many like to believe, and that is closer to the truth, is that Luke refused to continue the fight. Now imagine him as a Sith, and realize that upon meeting her, Luke might have allowed her in to lower her guard, and then picked his moment to cut her down or perhaps unleash a new Force power to claim her vitality in some way.
Those that want to remind us that Kylo Ren couldn’t dominate Rey and had to work to get anything from her during an interrogation might need to be reminded that as powerful as he was, Kylo was still a boy compared to Luke, since the Jedi Master managed to fool Kylo from across the galaxy. Had Luke gone to the dark side in the current canon it feels very likely that he would have been far too powerful for Rey without question, and might have even been a match for Palpatine at that time.