PvE = Kill another player and get baned from that group.
No. First and foremost it would open a new way of griefing, suicide into the path of someone speeding at a station, fly into the line of fire of someone at an RES, bait a newbie into attacking by pretending to be an NPC (a new player with no prior knowledge may not yet know what a hollow blip means), just to get them banned from PvE.
Imho a proper PvE mode should have all PvP damage disabled, this includes weapons and ramming, but keep the legal system intact, e.g. shoot a clean CMDR in Open PvE and you get wanted, but the other player doesn't actually get damaged. Thus you still have to watch where you shoot.