What if Mike Tyson had stepped into the octagon or maybe a K-1 ring? What if Bruce Lee had tested his mettle inside a cage? You can take any martial artist or boxer in history and as what if, but what you have to remember is the sport is called mixed martial arts. Anyone that comes into the sport with only one style of combat under their belt will not fair well and there are many example to prove it.
The thing with Norris specifically is that he isn't actually trained in many forms of martial arts, and what he is trained in is a lot for show rather than substance. His main base is a form of karate I believe and outside of Machida that particular martial art has never been successful in mma. He has competed in tournaments and from what I know did well, but there is a huge difference in competing against guys with the same background as you and using your skills for mma. That would be the same scenario if somebody who is extremely talented in judo or jujitsu came into the sport with only those skills. It wouldn't end pretty.
Honestly, it would mostly depend on when he got into the sport if he ever did. If he were to have any success it would be in the sports early days when fighters were far less well rounded and there were far less wrestlers in the sport. A strong wrestling base is the best base you can have in the sport at the moment, so even if he could turn back time and be a young lion again, without take down defense he would be screwed. Of course he was a natural athlete and has many accomplishments in the world of martial arts so you never really know. He could have picked up quickly on other parts of the game and done well. With what he has now though as far as disciplines go, they are lacking in too many areas to have success in todays mma game. Like I said, too much flash and not enough substance.
It's like Armbar and I have shared one brain since our online feud.
He's hit the nail on the head. I mean, even if you want to talk about Machida, who was successful with Karate, you have to remember that he has been wrestling Sumo since age 7 and also has a BJJ Black Belt under the Nogueira's. So even HE doesn't have one style. He also has that wrestling base that Armbar mentioned. That's why Machida was able to dominate against wrestlers like Tito and Rashad, they couldn't get him down because of his superior leverage (sumo) wrestling.
Even if you want to test things out in MMA with single styles. Look at Sokoudjou or as I like to call him Soko B. Ware. Black Belt in Judo....that's it. He got washed out of the UFC faster than Starnes after his fight with Quarry. One style doesn't cut it anymore.
Other than wrestlers you really need more than one style. Some wrestlers (Brock Lesnar) are good enough, big enough, strong enough, and physically gifted enough that they can impose their will upon their opponent on the ground. But wrestling, more so than all the other disciplines, frees up more possibilities. You can work a submission from the dominant position, you can work ground and pound, you can LnP. It's just an effective base.
Chuck Norris would not have faired well in MMA. Then again, his prime was probably right around the time that the UFC began, so...he probably could have done a little damage in their tournament format. He wouldn't have beaten Gracie, Shamrock, Severn, Coleman, or Taktarov.
I'll throw you a bone, though. If he would have entered UFC 3, I believe he could have beat Steve Jennum to win it all after Gracie and Shamrock pulled out.