Is defacing the airline logo of a wrecked airplane illegal?
In the US (you tagged your question FAA) it would most likely be illegal. 49 CFR 830.10 says (note that the NTSB investigates US accidents, not the FAA):


  (b) Prior to the time the Board or its authorized representative takes custody of aircraft wreckage, mail, or cargo, such wreckage, mail, or cargo may not be disturbed or moved except to the extent necessary:
  
  (1) To remove persons injured or trapped;
  
  (2) To protect the wreckage from further damage; or
  
  (3) To protect the public from injury.


It seems highly unlikely that painting over logos would be justified for any of those reasons. On the other hand, this wording leaves the question open of what might happen after the NTSB takes custody, and in theory an airline could do it with permission.

Personally, I find it hard to see how this would help the airline because the story would be all over the news anyway, but laws and attitudes vary widely in different parts of the world.