Yes.
I tried it on my ride today to confirm my memory.
It feels more natural to “kick kick” in the “down” phase of the post, but if i think about it I can do it in the “up” phase.
I can also do it if I am sitting, or if I am “standing” (two point).
This was all in my dressage saddle, with long stirrups.
( I don’t normally use a lot of “kick kick” for lateral work. My instructor generally wants me to do more with the position of my hips and my shoulders)