If you go back further to the Chonji kata of General Choi's Tae Kwon Do you will find a part of the Old Channan Kata. From what I understand Tae Kwon Do is Funakoshi's Shotokan Blended with the Kicks of Taekyon by General Choi in 1945 to form Tae Kwon Do. So my thought is yes Korean Karate. The story I was to is that General Choi was once a house servant for funakoshi while he went to school in Japan. That is how General Choi learned Okinawan Karate!
Hi Al---yes, that could very be---but it's not just that! The Pyung Ahn hyungs that were widely performed in the early Kwans that came together to form TKD under presure from the Korean defense ministry in the mid 1950s are none other than the familar Pinan/Heidan forms from familiar karate styles. The Palgwes and even the Taegeuks are basically rearrangement of familiar Shotokan kata (funny, today I was showing parts of some of the Palgwes to a student of mine, a Shotokan dan practitioner, and she kept saying, `Hey, we have that exact sequence in [such and such kata]').
And as far as taekkyon is concerned, you might want to take a look at Stan Henning's authoritative survey of the state of traditional Korean martial arts in the first issue of the 2000 volume of Journal of Asian Marital Arts, where he discusses the term `taekkyon' and shows that this term is based on erroneous interpretations, in early premodern Korean manuals of physical training and combat methods, of the meaning of certain Chinese ideograms. The correct rendition of the item isn't taekkyon, which seems to have a connection to the modern Korean tae `foot', but takkyon, `push the shoulders', about which Manning says `the term originally may only have been meant to describe a specific... technique to put an opponent off balance.' Takkyon appears to have been effectively suppressed by the Japanese in the 19th c.; taekkyon is an essentially modern discipline with no demonstrable connection to anything in Korean (pre)history. Bear in mind that Manning , a respected martial arts historian with degrees from the University of Hawaii, has based his conclusion on an exhaustive perusal of the full set of documentary records we currently possess on the topic---the full set of combat technique manuals published in Korea along with contemporary historical chronicles such as the Koryo History publishhed in 1451, which contains material going back to the 10th century, and the Encyclopaedia of Illustrated Martial Arts Manuals published by Yi Dok Mu in 1790---itself incorporated extensive material form still earlier Chinese sources, an important resource since apparently a huge proportion of Korean combat techniques have Chinese sources, not surprisingly. Mannings authoritative overview, BTW, concludes with the somewhat bleak assessment that `traditional [Korean] martial args... appear to have been almost entirely abandoned by the beginning of the twentieth century'. He rubs the point in that `the evidence does not allow us to say, as some claim, that the traditional military skill, subak, was directly related to taekwondo or that "taekwondo is a martial art independently developed over twenty centuries ago in Korea", citing a very commonly repeated bit of legendary history from a web site on TKD. His conclusion---supported by what looks to me like the most exhaustive survey of the surviving documentary evidence to date---is that `Taekwondo, for the most part,... appears to be a post-Korean War product, developed primarily from what the Koreans call tangsudo (karate) introduced during the period of Japanese rule.' The tradition Korean martial arts are but a vague memory and taekwondo a symbol born in the cradle of modern Korean nationalism...'
There's no question that something called taekkyon (very likely based, as Manning notes, on a Korean folk etymology of the last century) existed in the early 20th century as a combat system and that some of the Kwan founders practiced it, to one degree or another. But there's no evidence tying it to any ancient indigenous martial art of Korea. The vast weight of the evidence---especially the actual technical content of TKD---makes it clear that TKD is... well, karate as practiced in Korea.