Absolutely, but more so the clubs who pay his wages. There was a case in the UK a few years back where a player was found guilty of rape and battery and the team (Manchester United) was humming and harring so much so the teams sponsors threatened to walk away. The fans were pleading to get rid of the player with some hard core hoping he would remain. He was sold to another club in another country and his career is still ongoing, but never in England again.
When you play for a team you represent the team and if you beat up women or do something as bad then there is no place for you and it is that simple. You cannot separate the two as by keeping the player the owners of the club are condoning his actions. Funny enough the Green Bay packers are the same owners as Manchester United.
RE: Should leagues punish players for offenses that happen off the field?