“Administrative punishment” already includes the “relief for cause/lack of confidence” letter in his service record. If additional issues were surfaced in the more in-depth investigation, there could be a “punitive letter” put in his record.
Even though he will be eligible for promotion to flag rank at the regular time, the presence of negative material in his service record, particularly during major command as an O-6 in his warfare specialty, will 99.999999% cause non-selection. He can choose to remain on AD to 30 years at the rank of O-6, or more likely, stick around sufficient years to ensure he can retire as an O-6, then retire.
There are plenty of staffs where he could be buried as a section head, but he would never have command again. Of course, that is the reality for the majority of O-6s, but without major blots on their records. Normally, achieving the rank of captain and completing a tour of duty in major command is the epitome of a successful Navy career, as is leaving the service when it feels right to go, with a stellar record. Making flag rank is that extra swirl of whipped cream on the top.