You can still catch the legendaries in the sequel, all but Mewtwo in the original GSC games. Did he catch Mewtwo then? What about the others? Did he catch then release them?
In GSC, there are small references to think Red and Mewtwo did battle. But not necessarialy capture.
As for the sequels, such little hints and notes don't exist anymore, but I don't think there's a reason why Red couldn't have met Mewtwo there either. The guard lets you in the cave with the Kanto badges, meaning you are not the first one to go in.
