Hopefully you are as confused by all this as I was when I first started researching this...I even broke down and asked a few lawyers that I play the occasional round of golf with.
After buying these <ahem> gentlemen lunch and way too many drinks...
There are two basic questions that have to be answered:
1. Does the President have the authority to declare Martial Law?
The answer is yes. With the havoc caused by the Thanksgiving Day Massacre, the President did have grounds to call upon Congress to confirm a state of martial law.
Did this happen? Both the v.1 and the BYB fail to mention this confirmation. But the approval of the Senate is critical for such a declaration to be legal. Only Congress can declare a suspension of habeas corpus.
2. Did the President have the authority to name a military officer as a successor to the Office of the President?
The answer is no. The Presidential Succession Act is very clear upon the necessary chain to determine if someone can be named, and active military officers do not fall within the PCA. For General Cummings to be named as President, he would have to resign his commission, be appointed as Secretary of Defense or even be named Vice President before he could fulfill the provisions of the PCA.
For General Cummings to remain an active duty officer AND take the office of the President, the PCA would deny him the legal authority necessary.
In real life, MilGov would be the illegal government, at least as described in the canon material.