It would have been easier if the Confederate States Army crossed the border first, which was exactly the intention of the more militant leadership. They were expansionists and made no secret of their desire to colonize, by force, Cuba, Mexico and even all of Central America. They first had to dispose of the 'pasty-faced mechanics' in the Union Army which proved to be far more difficult than the Fire Eaters of 1860 promised.
I realize some thought they could conquer the territories, as indeed they tried to do.
But I fail to see how recapturing a fugitive slave from Kentucky who has crossed into Ohio would be easier after the South had won its independence. The only way that would work would be for them to conquer and rule the North directly, which kind of puts a crimp in their original justification for secession. Even then, they just move their problem to the Canadian border.