That would be hard to prove. Slaves were certainly imported illegally after the ban - it's one of the businesses Jean Lafitte was in - but I'd want to see solid, documentary evidence of slave importation in the 1850s.
Emancipation was accomplished in several ways and incrementalism was one very successful strategy. E. g., Pennsylvania, allowing slavery, despite its Quaker roots, eliminated slavery gradually de jure by recognizing the inalienable right to liberty to all residents born in PA. All descendants of slaves born in PA were born free. After a generation there were no more slaves in PA since importation of more slaves was banned as well.
The Civil War was about slavery, economics and political power, not states rights, provably so. Always go to the primary sources when researching history. Read the CSA Constitution. It’s online. It refused admittance to any free soil state and disassociated any CSA state which changed to a free soil state. Where is the “states’ rights” in that?!