Jeez, Drew. Whatever you do, don't ever ever ever call it that in front of a Korean. No joke.
I think that's what Koreans themselves called it back in the 1950s and 60s, because it was more like karate back in those days. A lot of them learned karate when Japan occupied Korea up till the end of the second world war. Modern TKD was modeled on it. Word!
But you are right, I don't think they'd appreciate anyone calling it that now. I trained in TKD from age 8 until I graduated from high school and never ever heard any of my instructors or their teachers mention Japanese karate or any connection to it.
Back to topic, I don't think any karate style is complementary to aikido. The movements seem too stiff and angular and idea of punching and kicking just doesn't fit in with blending. On the other hand, it wouldn't hurt to learn some decent punches and kicks to use as atemi to make aikido practice more realistic.