Yes, you get under (it feels as though your effective center of mass is lower than your partner), but there is no physical lowering of the body, and there are a number of different ways in which one can get under, of which I have described at least two. How do you generally teach people how to get under, and when they do, do you see a difference in how various waza are applied?
Yes, I would describe what is done is suwariwaza kokyu ho as a "floating" but you're both sitting on the ground (so you really can't physically get any further under your partner).
I think many Aikido techniques have an element of "floating". I personally don't feel that it's especially "internal" in nature. It does have lot's to do with being able to feel under your partner.