In a manner of speaking yes. Spartacus was under the impression that the woman he would have sex with was Licinia. Whereas Ilithiya was under the impression she would be having sex with Crixus. Both of their faces were concealed by masks so they had no way of knowing who was really behind them. And since they both hated each other immensely when they both found out who they were paired with they were both shocked and horrified.