The injury would have had to happen (and the team would have had to apply) before January 15th. At this point in the season, they could only get an exception for next season, and that would only be if Rondo were deemed to be out all of next year.
Its too bad too, because you can use it for a trade for a guy in the last year of his contract, which I hadn't realized:
The team may trade for a player in the last season of his contract only (including any option years), who is making no more than 50% plus $100,000 of the disabled player's salary, or the amount of the Non-Taxpayer Mid-Level exception plus $100,000, whichever is less.