Ok I found this at Army *******
“Individuals who are known to have tested positive for hepatitis C virus (HCV) infection require confirmatory testing. If positive, individuals should be clinically evaluated for objective evidence of liver function impairment. If evaluation reveals no signs or symptoms of disease, the applicant meets the standards.”
So to me that sounds like if you test positive for antibodies but not for the virus itself and have no liver damage you should be good to go.
You should ask the recruiter if you are eligible to enlist if you arecuredog Hepatitis c but still are positive for Hepatitis c antibodies. Even though you are cured you will always test positive for hep c antibodies.