Could I be eligible for a phone replacement if I file under a battery issue?

I just got my phone and I honestly turn off everything I need, only turning things on when I need them. I am aware of all background app refreshing, iTunes automatic updating & all the little things Apple has in their iPhones. I just got this phone 1 or 2 weeks only and I have noticed my battery just drops when I don't even use it. I would just leave it locked/on standby and I would check again and the battery would drop 2%. I would use my phone nonstop for about 5 minutes and it drops about 1-4% each time. I have an iPhone 5s that's brand new and I don't think it should be having issues like this.

Under the 1 year warranty, could I go bother the **** out of the people at the Genius Bar and have a chance at getting a new phone?