I figure that the Supreme Court could have been appealed to if the South had not seceded from the Union. But even if they did, the North did not recognize that as being valid. So the South always had a right to appeal to the Supreme Court. And what could the North have said? That it was legal for some states to wage war on other states because they did not like some of their practices?
I guess the role of the Supreme Court as being the arbitrator of Constitutional issues had not been firmly established by that point.
[Besides I can not figure out what the North was thinking. If the Southern States were still part of the Union, then how could one state make war on another? Is not that a violation of the Constitution? (And so what if the president orders it? So what? That does not make it legal.) So the North must have thought the South had legally seceded. Okay. Then they had seceded. Fine. End of Story. [I am not ignoring Fort Sumter. True that it had been attacked, but the North was not fighting the South to take back Fort Sumter!!]
(As General R.E. Lee put it ironically in one of his letters (I forget which one), the issue of secession had been "decided by arms."---i.e., it had not been decided at all.]