While he'll never be 100% free, long doses of time and a media which moves on will have a way of softening impact for the vast majority. Once this is over, the media will go back to talking about Brady as a football player, with less and less mention of the controversy and the general public hearing it will begin to dutifully revert to their previous position on Brady, whatever that happened to be, aside from the ultra haters who will never be convinced even if Goodell comes out and says the whole investigation was a complete sham. Ray Lewis is a good example, going from potentially charged in a murder to hero in a decade and getting a statue outside the stadium.
I think this is why the suspension is so important. If there is none, there is the potential for this to become truly a very small footnote, that might not even be mentioned in legacy pieces. However, if he does sit out a game or two, it's going to have a slightly larger impact, being mentioned any time his career is summarized, particularly after he retires.