I suppose that the main discussion over grease (not Greece!) is about the 'jampot' (wotsitcalled?) type of SDS - remember seeing someting about adding grease, possibly due to the right-angle drive.
For the in-line type, the only grease I've ever used is a bit on the drill bit or arbour of the tool. AIUI the action is like a slide-hammer, so the chuck needs to move freely on the tool.