They could certainly argue and disagree about the moral quandary of the week (which they did quite a LOT on TNG), but that's about as far as I would have wanted them to take it.
Certainly. However, it seems even that was a touchy thing with Gene. He didn't even like too much of that.
For example characters like Capt. Jellico or Adm. Pressman could have never been used while he was alive.