Umm

Until now it seems not, he could have recognized him from the beginning but no hint is directly thrown yet.

The other thing that worries me is the "never betray me" rule of their contract. If Lee Sa-Young doesn't know yet, does that mean he would consider the real identity of Cha Eui-jae as betrayal as he was keeping it in secret.. ? If not, in what matter that rule comes in the story if even does.. (=・ω・=)

Nahh, don't worry