There is a criteria used to determine who warrants a nomination for the Hall of Fame. One such criterion is integrity. And although, I do not believe a player's integrity-- the def. some use anyway, should not be a factor in electing a player into their sport's hall of fame-- a representation of the best atheletes of that sport, and not those who were good citizens, integrity applies, and by that criterion, Pete does not deserve to be in the hall of fame.
Pete Rose's case is however very different. His is an ethical issue-- he bet on the sport that he coached. As a manager, he had insider information, and to make matters worse, Pete bet on his own team. That is inexcusable as it goes against everything sports stands for.