It's a fine line and you have to be a good judge of character to take risks on guys with these kind of attitude blemishes, you also must have a solid grasp on the core of your team. This is something the Patriots have done well over the years, and I think DA has the same eye.
When asked about about bringing in players with character flaws, Bill Belichick often says things like "he cares about football, winning is important to him," etc. That, to me, is a key difference between guys who have made mistakes off the court (i.e., Birdman) and guys who just can't fit into a team concept (i.e., D. Miles) and are all out for themselves.
I think Birdman would be a cool addition. He has a history of being a popular teammate and being a great energy player and locker room guy, and hard worker. By all accounts, he is really no risk in terms of pure basketball. You obviously have to account for the off the court risk, potential relapse, etc., but if you can minimize his cost and be confident he's shown a commitment to stay clean, he could turn out to be a minor steal.