Would Beckham signing be good for Milan?

There are reports that Beckham will be training with Milan in January and “The Rossoneri” will try to make the move permanent.

Milan were after Beckham two years ago when he decided to not renew the contract with Real but the England international has chosen LA Galaxy.
The Rossoneri don’t have a right band player and Beckham would be a good option. This would be another big transfer move for Milan this season after Ronaldinho and Schevcenko signings.
Milan are in trying to reconstruct the team after a disappointing season when they failed to qualify for Champions League.

What’s really strange is that Milan are still signing old players when that are supposed to rejuvenate their team.