Alexander to the Bears?

Shaun Alexander was recently released by the Seahawks, and I'm just wondering if he'd be a good pickup for the Bears. Cedric Benson struggled last year, and maybe picking up Alexander would be a good backup. He'd be cheap, and would be a great backup &/or starter. Yea, he was injured last year, but who knows, he may have 2-3 years good years left.