CAS Trust say that relegating Charlton a points per game basis would amount to 'eviction' from the Championship: https://www.standard.co.uk/sport/football/charlton-championship-points-per-game-season-a4448371.html
The Trust says that the four misconduct investigations should be completed before any relegations take place (the one relating to Birmingham City is at an appeal stage and is likely to lead to a small points deduction, if any). These investigations are well behind schedule and even if they were completed any adverse decision is likely to be challenged in the courts by the club concerned.
Charlton are in no position to mount a legal challenge against any relegation decision. Whilst there might be a legal case for any club relegated out of the EFL because of their shareholder status, I am doubtful whether any decision relating to the Championship would be overturned by the courts. If the decision has been taken in accordance with League rules, the fact that a club would be unfairly disadvantaged is not in my view a basis for a legal challenge.
The best hope is that the season resumes. It seems that there is a contingency plan for doing that, but whether it is implemented remains to be seen.