Plaxico Burress was released from prison after serving a 20 month sentence. The 34 year old wide receiver is a little older and if the Bears were to sign him, he better be more than a little smarter.
The Bears have stood firm on their commitment to developing Johnny Knox, Devin Hester and Earl Bennett and Jay Cutler has shown that he can light defenses up without a "go-up-and-get-it" guy.
I don't think the Bears should sign Burress because he doesn't fit the organizational culture. The Bears want character guys and Burress is not.
Signing Burress would also slow the progression of the current group of receivers. This could also tempt Mad Mike Martz to go rogue with a pass happy attack and risk Cutler's health. The offense was more productive by being committing themselves to the run and featuring Matt Forte.
If the Bears pass on Burress, which I expect them to do, the current group better improve their onfield performance as there have been issues with route running, not fighting for the ball and getting jammed at the line of scrimmage -- all the skills that make Burress an interesting option.