I would say heck no in reality, but from what he showed last year, they wouldn't be hurting themselves too bad [they have Taj Gibson/Asik as backups]. I don't think the front office would take such a risk, and they are probably chalking up his poor playoff performance to his injuries.
I would argue that Boozer doesn't exactly raise his level of play once the post season rolls around... at least in the past five or so years.
But yeah, there's no way they cut him IMO.