Maybe, but there are reasons not to just go by the first thing you find on Wikipedia, and you've found a great example.
First, what's pretty definite about the Permian Extinction is that a really big meteor hit near Chicxulub, in the gullf of Mexico, at the right time to contribute to it. What's called the K-Pg boundry Iridium layer supports this.
Second, there's real doubt the big rock from space was enough to cause the known extinctions all by itself, so something else, such as Methane Clathrate release happening about the same time might be needed to explain some of it. That's two mights - we might need to consider more factors, and methane might be one. You're adding a third might, that the Methane might be a key factor, which I take to mean you think it's bigger than most, but not necessarily all of the suggested other factors.. There's lots of other possible factors, such as which continents were recently reconnected by land bridges after aeons of isolation at the time, or what did the evolution of flowering plants contribute, if anything. If you're right, Methane release is more significant than most such possibilities, but that's a long chain of mights, only as strong as its weakest might. .
I'll give you a countervailing wiki entry: https://en.wikipedia.org/wiki/...
The part about the Deccan Traps gives an alternative source for tremendous amounts of Carbon with a source which could change isotope ratios. Also, while I don't think the meteor itself could have had enough Carbon in its composition to make much difference, it is a known fact that stuff from elsewhere in the solar system can have different isotopic ratios. In fact that's one of the things the recent cometary probe lander was supposed to measure, so I supposes somebody ought to do a few back of the envelope calculations to really rule that possibility out.