That we will never know, cuz they failed. The attacks on Washington was also when the South was already destroyed. I seriously doubt they could keep Washington. It was more like they wanted to embarass Lincoln so he would lose in the next election.
There were political as well as military benefits to be gained. The Union, heartily tired of war, would be electing its President in November. The likely Democratic candidate, George McClellan, was promising a negotiated peace while Abraham Lincoln was promising to finish the war no matter how long it took. If Early could embarrass Lincoln, deepen the war-weariness and brighten McClellan's prospects, he might assure the survival of the Confederacy.
When Washington, D.C. Came Close to Being Conquered by the Confederacy | History | Smithsonian
What do you mean we will never know? You give the command to capture the president you are attempting to overthrow the government. That's plain and simple. You yank him out of the White house, government is overthrown. What you intend to do beyond that or how long you intend to capture the president of the United States is irrelevent.
But you say the goal is that by capturing the President of the United States of America they could embarrass America and get the leader in power they wanted instead? How's this not textbook government overthrow?