It can but there has never been a petition that was denied for an injury related reason. If it was denied then they'd ask for another player or use someone already on the 40 man.
These are revocable waivers. Last week the Halos put Tyler Anderson on waivers and nobody claimed him so he was kept. However if they get rid of all of these players it will knock them under the CBT tax crap, um cap.
One thing to remember is these players do not gave to be released if they clear waivers. They can remain with the team if the team wants them to. Except Donaldson. I think he went on release waivers.