“Can private sector lawyers represent defendents in a military court?”
yes but its not advisable unless they know military law
Which this one does.
Still, while the accused (in legal terms) is allowed to have a civilian attorney, he is not required to have one, or have one appointed for him. He gets a JAG officer do defend him. So if no one would take the job, he'd still have the "Assistance of counsel for his defense" as required by the 6th amendment.
No body can need the money so badly, especially not retired military, to defend this slime. The JAG officer will be ordered to defend him, so that's OK. But this guy should have refused the job offer. I imagine it will be like "cleaning a porta potty with your tongue" before it is all over. "the accused" will probably blow up and fire him anyway, before it's all over.