Would they have left if Breckenridge got elected?
Probably not. Those advocating secession needed some sort of event to rally around, and they chose Lincoln because they could construct a narrative that people in their states might believe.
Just guessing. I don't know for sure what they would have done, but you can bet they noticed how much vigorish they were paying to New York and Washington. I think they would have tried something at some point in the not to distant future from 1860.