I think you will struggle to see enough noticeable change in the mirror to keep you motivated. When I've lost substantial weight in the past, it can take months for me to perceive any noticeable difference, whereas the scales would give me feedback on a weekly basis.
Have you tried it? I feel like kettlebells are one of those things you have to try to understand, there's such a "WTF" factor involved in them. If you try one and still don't like it, don't use them, there's plenty of ways to skin a cat.
Yes, your jogging is becoming more and more useless. The reasons TX Iron above gave you may, or may not be valid, I'm not smart enough to know. In my limited mind though, the evidence is pretty clear. People who I see jogging, almost universally, look shit. Especially those that do it at a very high level. This tells me that getting really good at jogging does not make you look better.
All muscle is functional, depending on the function you want it to perform. Defining something as "functional" without defining the function is meaningless.
And the answer to your question is: It doesn't matter. When I do jump rope, I do it as part of my conditioning before I lift, but it really doesn't matter