What a bunch of crap! The importation of slaves was ended in 1808 and the slave population of the US grew by nearly 4 times from slightly over 1 million in 1810 to nearly 4 million in 1860. At the heighth of the Underground Railroad, only a few thousand slaves escaped each year. And with the slave population increasingly concentrated in the deep south cotton belt, the chances of any slave making it hundreds of miles to freedom in the north were slim to none.
The slaveocrats banned importation of slaves in the Confederate constitution for one reason --- it was in their economic interest to do so. If more slaves were imported it would decrease the value of their existing slaves. That is not even to mention that the Atlantic slave trade was all but dead by 1860 thanks to the efforts of the British Navy. That clause was like giving up Brussels sprouts for Lent!
This southron canard gets repeated over and over and over until it is accepted as gospel, just like the ridiculous claim that the south paid 85% of the total tariffs. The actual fact is that, far from banning imports, the confederate constitution actually protected imports. Article I, section 9:
The importation of negroes of the African race from any foreign country other than the slaveholding States or Territories of the United States of America, is hereby forbidden; and Congress is required to pass such laws as shall effectually prevent the same.
CSA Constitution Section 9.1. The importation of negroes of the African race, from any foreign country, other than the slaveholding States or Territories of the United States of America, is hereby forbidden; and Congress is required to pass such laws as shall effectually prevent the same.