Ehh, after thinking about it, I'm not so sure. If this is the predictable shounen which I expect it to be, Erina will spend some time in denial of how someone like Souma could be related to her idol, she'll throw some insults, eventually she'll accept it, but still won't accept Souma, and... nothing would change. Hopefully something different happens.
By the way, what's the anime in your signature?
It won't be predictable because it's not only Erina that is there, her father is as well and we don't know how he would react to such confession.
He has two routes;
The good - He will believe 100% that he is the son of his senpai. He will ask few questions about his father and what is he doing in life atm. Souma will, of course, answer and tell him that he owns a local of food and he might be disappointed by it. He'll also consider souma a dangerous person to deal with so he will act quick to kick him out of the school or he might manipulate him in someway. He could also try to fool him by telling him he will train him to defeat his father, idk.
The neutral - he won't believe what souma is saying and then he will leave. Erina will also wont believe souma's confession but she will keep it in mind for couple of days (in manga format) and she will forget about it. If she does meet again with souma's parent, she might ask him or he will tell her right away and from there we will see some predictable moments between erina and souma and we might get some goodie development.
I believe that azami will try to do something bad towards souma so souma's dad shows up and have a duel, 1 vs 1.
Anime is Nabari no Ou
[video=youtube;YQYD6UKJ2wk]https://www.youtube.com/watch?v=YQYD6UKJ2wk[/video]