I see no benefit to putting the entire kit in a group, personally. Not for live anyway.
I regularly put everything but overheads into a subgroup for parallel compression. I tend to compress the overheads a bit more to begin with but the other gives a nice fat sound on the whole kit. That subgroup then gets mixed in to taste depending on the feel of the song.
VCA/DCA's are a different matter. The whole kit goes in one. My regulars are Leads, BgV, VoxFx, keys, gtrs, bass, drums and spoken word. Subgroups on leads, BgV, parallel drums and spoken word at a minimum. Patch a deesser and eq across the spoken word for feedback control and universal de-easing where you have limited processing. Use a sidechain filter on a normal comp with fast attack and release to make a de-esser if the desk doesn't include one (like the gld80 I was on this weekend).