No, it wasn't. New York was 800 miles closer than Charleston, it had better harbors, better docks, warehouses and every other sort of facility. New York had plenty of natural advantages to induce traffic to go there. The laws just made it so that other ports couldn't compete with their natural advantages.
The only thing that could have induced people to carry shipping traffic 800 miles further to the South was a greater profit, but so long as the Navigation act was in effect, It was hard for foreign ships to make profit going an extra 800 miles to have to pay the same tariff duties.
With Foreign ships effectively kept away from visiting these other port cities, American ships could use their monopoly to price gouge way above the market value of the free market.
Change the cost of the tariff duties, or allow foreign ships to visit more than one port, and suddenly it becomes very profitable for them to go that extra 800 miles.
Who hauled 75% of the cotton crop to England and France.