I don't think the Saturn's fortunes change too much in this scenario. The main problem the system had was a lack of good games, especially first party games. The Saturn actually had a killer app in Japan early on which was Virtua Fighter. Consequently, the Saturn did fairly well in Japan. It didn't do well in the rest of the world, because they didn't have a game that other regions considered a killer app. What they really needed was a great Sonic game. A more interesting alternate reality would be if Sonic Mania was released on the Saturn back in the day. In that scenario, I think the Saturn has a fighting chance.
The only problem with that is at the time every franchise was making the jump to 3D. After Super Mario 64 marked Mario's 3D debut, and basically revolutionized the industry and helped set the standard for 3D gaming, everyone was naturally expecting Sonic to make the jump. Because the Sonic vs. Mario rivalry was still very much in full effect at this time (Sega does what Nintendon't). And that's where Sega floundered and struggled because it took them longer than they could afford to make the proper transition. By the time Sonic Adventure finally dropped on the Dreamcast, they were already past the point of no return. All it ultimately did was provide more life support for their already dying console business. If they had developed a proper 3D Sonic game for the Saturn instead and got it right, I think that would have benefited them MUCH more than if Sonic Mania was on the Saturn. If they had done that latter, Mania still would've been the great game that it is now, but it wouldn't have been received with nearly the amount of praise and acclaim. In fact, it might have been viewed as a disappointment because Sega opted to play it safe and make another 2D game instead of shooting back with their own "Sonic 64" like game.
Hardware Comparison Threads:
PlayStation/Xbox/Switch Hardware Battle: 2021 Edition!
PlayStation 4/Xbox One/Nintendo Switch: 2019 vs. 2020
PlayStation 4/Xbox One/Nintendo Switch: 2018 vs. 2019
PlayStation 4/Xbox One/Nintendo Switch: 2017 vs. 2018
PlayStation 4: 2015 vs. 2016 vs. 2017