I don't know if it will change much. Naruto is gonna be angry/sad, and they'll comment that despite losing the girl he loved, he didn't become like Obito....
I doubt much would change. For example, Neji's death came and went without much of an impact, and I expect it would be the same if Sakura were to die. Granted, she's a main character but she hasn't done much for viewers to grow attached to.
It might cause Naruto to become enraged, but it would be nothing more than losing a comrade since he seems to have already acknowledged Hinata.