Do you believe Machida's success in mma is due to his karate training? Kata?

Well karate is a holistic training method, so if the question is whether part of his fighting prowess revolves around performance of solo routines i'd have to say no.

However if you mean depth of understanding and usage that can come with karate training, which can be kata-driven, then i'd say sure. A whole lot of fighters got their start for instance in Kyokushin, however it seems to be the popular thing today for people to minimize the effect this training has had on their MMA careers, or maybe it's just the fans that do that, I don't know.

There actually have been Karate/MMA crossover people here and there as long as I remember in MMA (look up Joe Pomfret - a Uechi Ryu and BJJ guy for one random, not so well known old school example), but as I said people seem to like to minimize the effect of Karate training in such an environment, whether justified or not.