It's probably part of the reason for MMA's birth and popularity. I think Bruce Lee (and a few others, but primarily Lee) popularizing martial arts in the U.S. and introducing fictional style vs. style tournaments (Enter the Dragon) is even more fundamental, though. In Japan, pro wrestling definitely gave birth to MMA, but the UFC itself isn't a direct descendent like Pancrase was.
It all goes back to Karl Gotch and Billy Robinson, who trained together in old school catch wrestling, both went their different ways in the pro wrestling world and ultimately both of them ended up in Japan training pro wrestlers.
Gotch trained Yoshiaki Fujiwara, who trained Suzuki and Funaki, who recruited and trained Ken Shamrock, Frank Shamrock, Rutten, going on to found Pancrase. Robinson would train most of the UWFI wrestlers that would go on to become Pride.
Then I don't think a lot of modern fans really understand the influence that Rings had on Pride. Pride basically swallowed up Rings, took their best fighters(Fedor, Overeem, etc), stole their ideas, then put them out of business in 2002, right around the time that Pride really started to kick ass.
The guy who founded Rings, Akira Maeda is connected to Takada, Fujiwara, and Tiger Mask. Those four guys all came out of the same dojo and basically laid the groundwork for what MMA would become. Their bidding war over Rickson Gracie would basically shape the history of MMA.
If you take away pro wrestling's direct influence on MMA history, you take away Ken Shamrock, Dan Severn, Suzuki, Funaki, Frank Shamrock, Bas Rutten, Sakuraba, Takada, Fedor, Pancrase, Pride, Rings, Shooto never happens. I think it's safe to say that maybe MMA never happens, especially when you consider the influence that pro wrestling had on Mitsuyo Maeda, who taught the Gracies how to grapple.
Maeda was living in a YMCA in Alabama at one point during his travels, learning tricks of the trade from the pro wrestlers he befriended in the 1900's. He basically taught the Gracie's Judo with some old school pro wrestling tricks and submissions worked into it. I mean, if you take all of that away, what does that leave MMA? It would have basically been just a toughman contest, it would have died an early death, if it even would have happened at all.