Yes, technically he may plead the fifth because adultery is still a crime on the books in South Carolina (although there have been no recent prosecutions for it in recent years). However, in Family Court in South Carolina, it is permitted for a judge to construe pleading the fifth in response to an allegation of adultery as an admission of the adultery. As long as you have sufficient proof of "opportunity" and "inclination" that your husband committed adultery, his pleading the fifth rather than admitting the affair should not prevent you from being able to obtain a divorce on that basis.
Attorney Nowell gave a good explanation about adultery and pleading the fifth, and how the judge can interpret that as evidence your husband did commit adultery. I am licensed in CA and MD, but not in SC. In CA the courts could care less about whether or not adultery was committed, but in MD adultery is still considered a crime, although it really is not prosecuted. So it appears that SC and MD have a similar approach to adultery and taking the fifth. I suggest you consult with a local SC attorney to get the good legal advice you need.