The south was threatening to secede before Lincoln was elected, and mostly did before he was sworn in, which was 4 months after the election, not two like now. It wasn’t exactly a secret that war was a possibility. Faced with the possibility of war, why wouldn’t the War Department order their best general to Washington? So no it doesn’t imply what you infer.
Without sending that fleet of ships with orders to attack the Confederates in Charleston, there would have been no war. The South didn't want a war, but they had no intentions of being a rug either.
Almost all of Lincoln's cabinet advised him against sending that fleet of warships because they all believed it would start a war. Major Anderson in command of Ft Sumter wrote that it would start a war.
No Warships, no War. Also misleading the South and making promises they had no intention of keeping was also a contributing factor to the war.
https://chroniclingamerica.loc.gov/lccn/sn82014760/1861-03-11/ed-1/seq-2/