Export DC behavior to an animation

Is it possible to have the behavior of a DC included in an animation? I can see the animation in the model, with the “interact with DC” botton, can I export it to an animation or include it into a larger animation? For instance, doors opening in a house walkthrough animation.
In my case I am interested in including a push and pull in my animation: I have a rotating cube, then it stops and a smaller square appears on one the cube’s top face. The corners of the cube and smaller square overlap; then I push down the small square to carve three planes of equal thickness. How can I include this behavior in the animation?
In case you wonder…it’s for my logo.
Thank you