She may garner more attention when she goes to school and Keitaro would probably recognize her much sooner. It probably won't change the intro between Naru and Keitaro in the hot spring since I believe it was mostly because of the steam.
The biggest change would be after Naru failed the Todai test the first time when she takes her small trip. She'll recognize Keitaro right away and probably try to avoid him and that'll change how they'll interact with each other down the line because I believe them actually enjoying themselves without each recognizing who each other is what laid down some basis of their relationship.