The ability to carry on a war only becomes relevant if the Union first comes up with an effective strategy for war.
If the United States government accepts the neutrality of Virginia, North Carolina (agree with you on that), Kentucky, and any other border states which choose to remain neutral, the Union has very limited options. They could impose the blockade and try to secure key points along the coast like Port Royal, Pensacola, Ship Island, etc. as bases for further operations. Perhaps they could 'starve out" the Confederacy by cutting off exports (cotton) and imports, but that would likely be a prolonged process, uncertain of result, and hardly likely to inspire ongoing popular support. Use of the Mississippi would depend on the attitudes of Missouri, Tennessee, and Arkansas. And any effective action would likely push the neutral states into outright opposition and secession.
If they were going to allow states to remain neutral, what about Maryland? The federal government could be in the odd position of not being able to bring troops to its own capital.
If states could opt out of Lincoln's call for troops, how would that affect recruiting in the north? States or individuals who remained loyal to the United States might still be reluctant to commit troops/themselves to war once it became clear that they didn't have to.
A buffer zone of neutral states might be the best defense for the seceded seven.