Absolutely, you can teach and drill applications sans kata. Some people call this 'self-defense'. It's always amused and saddened me that many school's self-defense has no link whatsoever with their kata/hyung. The key to making this work, of course, is to drill it over and over again, with or without kata.
The point I'm making with bunkai is that if you have kata within your curriculum, your basics need to align with your bunkai. I've seen one of Mr. Abernethy's demonstrations where he essentially executes sankyo, a wrist/arm lock, as an interpretation to a movement in the Pinan kata. I believe you have to train sankyo (along with other grappling basics) to be able to pull it off. You can't do it, just because it is in the kata, or because Mr. Abernethy shows you how to do it a few times in a seminar. You must train it, and then it becomes a gateway to you reaching the same destination that Abernethy did. That's a subtle distinction, but I believe it's there.
I still don't totally understand which takedown you are talking about, but as an aikidoka, I simply don't believe one can just pull a technique here and there out from aikido and make it work as a karateka. You can hopefully find a technique that is close to the movement principles you practice already and then adapt it to your own usage, but it likely won't have the same feeling or level of effectiveness. To learn locks and takedowns, you MUST practice locks and takedowns. Generally that means you must learn at least some of the principles that perhaps you have not worked with before in your striking system.