I was the one suggesting GCTA in addition to GEMMA to deal with relatedness. I am not as familiar with GCTA, but GEMMA deals with case/controls as if it was a quantitative trait, using the following justification (from the manual):
"For binary traits, one can label controls as 0 and cases as 1, and follow our previous approaches to fit the data with a linear mixed model by treating the binary case control labels as quantitative traits [? ? ]. This approach can be justified partly by recognizing the linear model as a first order Taylor approximation to a generalized linear model, and partly by the robustness of the linear model to model misspecification [? ]."
This workaround was, I believe, an implementation convenience from the point of view of efficiency. You could use the same argument if using GCTA.