No it didn't. In fact, the properly elected and seated members of that government were prosecuted and penalized repeatedly and their authority overrun by military coercion with the sanction of Lincoln. Lincoln unilaterally and unconstitutionally suspended habeas corpus almost immediately after the war broke out and used it to silence both his critics and those who acted to impede his waging of war. Properly elected members of the Maryland legislature were imprisoned and others were sent fleeing from Annapolis under threat of having the same done to them.
One of the worst cases happened in Missouri, which, at the opening of the war, had decided to remain in the union and declared its neutrality in the conflict like Kentucky. The Missouri government called out its state militia at the beginning of the war and stationed them in St. Louis with the task of keeping the arsenals from being taken for use in warfare on their soil. Lincoln's army crossed into the state, violated its neutrality, captured the militia, and marched them through St. Louis as prisoners. When civilians came out to the streets in protest, the army opened fire on them killing several. This incited the Missouri legislature, which had previously voted NOT to secede, to organize troops in opposition to Lincoln's violation of their neutrality. The feds responded by marching the U.S. army on the state capital to oust the governor and state legislature!!! As the state militia organized to hold off the army, the legislature and governor fled the capital toward Arkansas. The state government convened in October in the town of Neosho, where the previously neutral legislature that had decided earlier not to secede drafted an emergency resolution and voted to join the confederacy. The secession ordinance explicitly stated their purpose of doing so - their lawfully elected government and lawfully convened state militia was literally being attacked and overrun by the federal army!
Similar abuses by Lincoln reached into the highest levels of the government. On the outset of the war, he had a U.S. Congressman from Maryland arrested and imprisoned. A few years later federal troops arrested and deported the leader of Lincoln's critics in Congress, former Rep. Clement Vallandigham of Ohio. In May of 1861 Lincoln even ignored a Federal Court ruling by Chief Justice Roger B. Taney overturning his order to suspend habeas corpus. In any other time, this would have been an impeachable offense. And that goes without mentioning that some evidence exists that Lincoln or others in his administration were even considering, at one time, arresting Taney himself over the ruling.
Now, if none of that is a disruption of the way our Government operates and operated, I do not know what is!
Also, no contingency of war prevented Jefferson Davis from appointing federal judges, etc.
Actually, one did indeed exist. It was called the Confederate Senate and it actively sought to halt judicial appointments out of fear that they would be used to assert national control over the state militias, which many governors wanted to control themselves.