While Lee's philosophy about aliveness and formless training may have been influential to the traditions now found in MMA, I would actually argue that without Bruce Lee, we might have gotten to this point in MMA a lot more quickly.
It was his movies that desensitized the American public to a very certain kind of violence: pretty choreographed bad guy/good guy violence. In my eyes, it's this expectation of a certain kind of encounter that jarred and repulsed so much of the populous when they were exposed to actual vale tudo combat, which, as we all know, can often be anything but pretty to the layman.
If we hadn't had this kind of nonsense filling our head when we first all got exposed to UFC 1, it might have been a bigger eureka moment for a lot of people, rather than the "OH GOD, those guys aren't doing kung fu. That's just street fighting" response that MOST people made before they actually had tried out their Wing Chun on an alive opponent.
Sure you can argue that Bruce's movies inspired a lot of people to take up martial arts, but they probably inspired a lot of people to believe a bunch of bullshit too. And since I think it's agreed we would have eventually gotten MMA anyway - since it came from a Brazilian family doing a Japanese tradition, not a Chinese guy breaking tradition on TV - it probably would have been better for most people to come watch UFC 1 with 0 preconceived notions of what combat should and shouldn't be, rather than their lofty dreams of Hollywood-come-to-life smashed against the hard pavement of reality.
LOL. Shaw Brothers and Jackie Chan are the ones that desensitized America not Bruce Lee or Chuck Norris for that matter. Their movies were not pretty at all.
He did not do the BS that is equated with "that isn't real kung fu."
But this is all kind of beside the point. The thrust of my comment is that, at least by their movies and acting, Norris or Lee can't be credited with much of anything besides an Emmy.
With or without Bruce Lee, I don't think America was ready for the protracted jiu jitsu match type of NHB fight. Without an Asian martial arts reference point, the public would probably view early MMA under a boxing lense, and from that perspective we'd probably still heard a lot of "get up and fight like men!" kinda stuff.