Yes, but you will have to prove it. There was a recent SC case on a similar issue where the employee refused to get a flu shot. See AnMed Health v. South Carolina Dept. of Employment and Workforce, 743 S.E.2d 854 (Ct. App. 2013). You may need medical or expert testimony to prove you case. I suggest consulting with a lawyer experienced with seeking unemployment benefits.
The foregoing is for general information purposes and does not establish an attorney-client relationship.