They could certainly do so for the fees incurred in the USSC appeal. I don't see the Supremes taking this up as the appellate decision was clearly correct on the merits.
Fighting words are not usually held to be protected under the 1st Amendment.
According to the article SCOTUS has agreed to hear the case. How do you see what the enbreeded droolers do as differing from cross burning, which the SC has found not to be protected speech?