Probably. The guy lied about gambling, then lied about gambling involving his team. The last claim he made was that he never bet against him, but it easily could've been a lie. Then again, it was the Reds, he had a .525 record and never made the playoffs. Either way, it was a violation of the rule.
Rose earned his hits and should definitely be in the HOF as the all-time hits leader. Now that he's dead, there's no reason not to. As I said, Shoeless Joe's guilt is more difficult. He confessed his guilt in throwing the 1919 Series and at least knew that the team were accepting bribes, because he himself had been offered multiple bribes.