From a personal POV, yes he should have because Arohi needs to hear this from him. Hearing it from someone else is going to hurt her more because she will feel as if Arjun is no longer trustworthy. But from the show POV, maybe not so soon. I think they will try to build up another track. At some point during today's episode Arjun did think to himself that him and Arohi can't be together even if they might want to. So, in a way he thinks its just not possible because they come from totally different families. I have a feeling that she will find out from someone else and will be angry with him for a while.
Maybe even from Gauri.(That's unless Rajvir didn't tell Gauri who Arjun really was...I can't remember)