More would need to change for Sega to not drop the ball. Sega made a ton of mistakes outside of price and Genesis Add-ons. If they do the following things outside what the OP said:
-Make it much more 3rd party friendly.
Before the Playstation console manufacturers were very strict on what can be made on their consoles. This included Sega. The best way for Sega to win here is to drop those restrictions. This would give the Saturn a huge library. To give you an idea of the number of games that could lead. The PS1 had about 1500+ titles released on it. The Genesis had about 700+. The Saturn had about 1000+ games but only 258 reached America. They would also need to start making deals with 3rd parties to avoid Sony's moneyhatting everything.
-More enticing 1st party games
Sega did a good job in the Genesis days but the Saturn really needed a big seller. The fact that Sonic never came made you question their decisions. What Nintendo was able to manage with the N64 was impressive despite having a lot fewer titles to work with. If Sega could do that + 3rd party support it would sell MUCH better.
-Don't be so Japan-focused
It was during this era that Sega of Japan made all of the big decisions despite Sega of America being much more successful. So we got a weird situation where Saturn was more successful in Japan but less so in America. The complete opposite of what happened with the Sega Genesis. Keep in mind that the PS1 and Saturn were neck in neck in Japan for a while until PS1 pulled ahead thanks to games like Final Fantasy VII.
If were to happen then we could see a situation where Sony has a harder time gaining traction. Sony would have to share a lot of the 3rd party titles that would be so popular with them. Sega could have won in this situation but I believe it would all depend on how strong the 1st party support would be.