I don't believe that there have been any reports that the tower was shut down or that approach/departure control shut down.
Pretty sure if you had a private plane, or a cargo jet that wasn't under the command and control of the flight opps of the major carriers that went dark, you could take off no problem.
If you wanted to sneak out of there the chaos created by the fire would offer a nice diversion. There would likely be very little scrutiny of any aircraft able to leave as they needed as much free space at the airport to park all of the inbound flights that no longer had any open gates to park at.
If something fucky snuck out of there that CAL 747 would certainly be the 1st one I would dig into.