I am a practicing lawyer also and whoever is advising Brady isn't giving him good legal advice. First, as Richlaw said, a Federal Court is highly unlikely to overrule the NFL's decision unless Brady can show the NFL acted capriciously and arbitrarily. Great deference will be given to the NFL because there is a CBA in place.
As for a temporary injunction, that is a pipe dream. It is highly UNLIKELY that a Federal Court will grant a temporary injunction. To obtain a temporary injunction, Brady must establish two elements. First, Brady has to show that he will suffer irreparable harm if an injunction is not granted. Brady can't meet that burden because Brady can be made whole at the end of the case without an injunction -- for instance, if the suspension is overturned at the end of the case, the NFL will be required to pay Brady's game checks for the 4 games for which he was suspended. Thus, he can be made whole without an injunction. Second, Brady has to show that there is a great likelihood of success. Given the state of the record, he can't make that showing either. In addition to the prima facie evidence of cheating, the record is clear that he intentionally destroyed evidence and obstructed the NFL's investigation. Thus, it is highly unlikely that he could demonstrate that the NFL's decision to suspend him was arbitrary and capricious. He's done folks. He is not playing week 1. Nor is he playing in weeks 2, 3 and 4.