If his uncrossable line in the sand is turning over his cell phone and email, suing the league is the last thing Brady is going to do.
Assuming he gets past an NFL motion to dismiss, the first thing the judge will tell him to do is turn over his cell phone, email, and all other pertinent documentation to the NFL as part of the pre-trial discovery process. He won't be able to refuse then, or he'll end up in jail for contempt.