No. It refers to a supposed part of the process of joining the Freemasons. The members of the lodge vote anonymously whether to accept a prospective member by depositing a white or black ball into a closed box, with the black ball representing a “no” vote. So “blackballed” refers to some exclusive group excluding outsiders.

I’m not a Mason so I don’t know if this factual, but that’s the idea.

Of course, someone could be blackballed because they are black—if a particular Masonic lodge had racist members—but it’s not inherent to the concept.