Possible, but I doubt it. Confederate sponsored slavery in say Arizona and New Mexico was purely theoretical anyways and thus the loss of these areas as potential slave states would not directly impact the South. Banning slavery in Missouri would have a larger impact, but Missouri was not the Dixie heartland and I think the south would reluctantly accept the loss.
In the end, the additional pressures that led to the war were not present in 1820 (Kansas Missouri border war, the caning incident in the senate, increasing northeren economic prowess etc.)