I can't say with certainty that slavery would have ended more quickly and more completely if the South had been allowed to leave and escaped former slaves had been allowed to remain free, and the North and the rest of the world had been a positive influence on the South. However, it's certainly a possibility that it would have ended sooner if the southern slave owners had agreed to a system of compensated emancipation and freed the slaves without a war and without secession, as most nations that ended slavery did. That absolutely would have been preferable to the Civil War as it happened.