You really have to draw a distinction between taking influence from MMA, and actually 'working' a mixed marshal arts contest.
They briefly experimented with "working" MMA contests in Japan, and it was a massive failure. The simply truth is that MMA as an athletic sceptical is not very entertaining to watch. As a medium it is dependent on what JR would call "smash mouth" moments, and if you remove the violence factor then people don't want to watch it.
The only way it could work is the way pro wrestling originally did, with people not being made aware that it's a work. When MMA was originally being conceived and high profile fighters from different disciplines were holding contests then I understand some worked fights took place, but in this day and age a full scale deception would be impossible to maintain.
The idea of a worked wrestling style influenced by MMA is considerably more plausible however. Today's product in America can essentially be traced back to legends like Ed Lewis taking armature wrestling, and adapting it to be more palatable to the crowd, with much less time locked up on the ground, more impressive throws and so forth. In Japan Inoki did something very similar, except pioneered a style that was also heavily influenced by marshal arts, focusing on stiff strikes, legit and semi legit throws, amateur wrestling techniques and submissions.
Nobody's going to mistake the Inoki Strong Style for a legitimate MMA contest, but it borrows from alot of the same influences, and is part of the reason why wrestling in Japan is treated as far more of a legitimate contest then in the US (KENTA not attempting to run Missawa over with a monster truck is the other part

).
If you ignore the luchadores, mainstream wrestling in Japan traditionally occupies a middle ground between strong style and more traditional pure wrestling. Under Inoki's tenure of New Japan attempts were made to push the strong style harder, but I think a process of trial and error has established what they produce now to be the most profitable style to pursue (although the Gate's sudden explosion might be moving to change that).
As for weather or not this could be adapted to suit a US audience, I'm going to say I don't think so. Certainly not in either of the main promotions. The simply truth is that people are not going to buy into a more legit style whilst "incidents" are going on backstage that openly scream "This is all fake, you're watching low brow comedy".
For today's story driven product, the basic superman vs super-villain is going to outdraw anything that transpires inside the ropes. You
could get the entire rosta of WWE/TNA working strong style, but it's not going to make it any more popular, and would be much, much harder on the bodies involved.
So to give a one line answer, worked MMA doesn't work. Wrestling influenced by MMA works very well, but it would have to be in a promotion where wrestling was pushed as a legit sport, and we don't have on of those.