Um, he didn't have a Rank in the ST:VOY pilot episode - he was just an 'advisor'.That's never stopped anyone before, especially if you have connections. Apparently you can be convicted of treason and get back in. (Tom Paris)
Janeway reinstated him to a field promotion after they were 70K+ LY from home. Remember, even the Maqui on the ship supposedly ALL had prison sentences waiting for them on their return home. <--- That was mentioned the first season on VOY a few times while I was still watching it (quit after "The 37's").
Given the era and the situation - I don't see Burnham ever being reinstated to Star Fleet as an enlisted/rank holding crewman anytime in her remaining lifetime (character wise.)
Lorca feels her intelligence and experience are still useful to his war effort, but even he did feel it proper to give her a ranked re-commission.