You could be right, however I don't know if he'd want to go against the Council, and he said himself he doesn't believe he is qualified on his own. It could be he meets with Martha, Eb, and Rashid and makes the decision to tell.
Martha wasn't injured. Unless she just didn't make it back to Edinburgh - in which case, who ratted him out over killing the turtlenecks? - the unanimous vote to put him on capital probation implies his display with the little folk and his actions during the battle scared her enough to flip her vote against him.
Eb is probably also going to be outright adversarial once the engagement to Lara gets announced.
Rashid is the only one of their pseudo-bloc on the Senior Council who would probably still speak in Harry's favor to LtW, assuming he's even one of the ones LTW felt obliged to consult. I'd bet River Shoulders is another outside the Council, so training with him to establish further trust would probably be a step in the right direction toward being clued in.