Barring a customs house at every road, railway, and river across the border stretching from Virginia to Arkansas, then no. They couldn't cover them all.
Looking at a map of the railway system in the U.S. around 1860 would indicate that there weren't that many lines connecting the North and the south.
But there was one great big line of another sorts. It was called the Mississippi River.
Make them two countries and it wouldn't be hard for the government to limit the available crossing points and slap a tariff on the goods as the came across.
Not really. That would have required controlling every crossing of the border all the way from Virginia to Arkansas. Discount that fact as you may, but it simply wasn't possible. For example we can't even control a border today with all our modern technology - not even with the help of a large river running along it and the fact that 90% of it is out in the middle of a desert to nowhere. What makes you think Abe Lincoln could have done the same across the north-south border from Virginia to Arkansas in 1861?
But if the buyers up North knew that the goods would be hit with a tariff as soon as they brought it up North then why would they want to pay the confederate tariff, the U.S. tariff, and all the associated transportation costs?
Because it was logistically possible to transport those same goods up north while avoiding the tariff.
Every road? How much travelled by road in those days?
All it takes to get it across the border is a couple of miles, so you tell me.
So how much moved by road those days?