So lets say that the white cube is at the world origin. And you want to rotate the camera around it with the pivot point of the camera at the origin too. Where is the grey cube in the world that it could remain always in front?
This is a spatial problem and the only way I can see Blender doing this is if you put an image of the cube on a card (with an alpha) and have that card be fixed to the camera or always facing the camera. (both easy things to do in C4D).
If you don’t want to render out the grey cube to have a texture to put on the card, you can use the Camera Shader to look at the grey cube that is somewhere off camera and then use that “view” as the source for the material for the card that always sits in front of the white cube. This way it can be live and any animations you do on the grey cube will instantly be populated in the material you put on the card.