Bruce Lee was picked up and played with by "Judo" Gene Lebell.
There were 33 grappling techniques Bruce put in JKD before he died. However, grappling did not become that great of a need till after 1993, when BJJ showed it's mastery over striking arts.
Dan Inosanto, Bruce Lee's right hand man in JKD is a BJJ Black Belt.
As for being in the Cage, I'm sure Bruce Lee would do well in his prime. He is as per Dana White, "The Godfather Of MMA".
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