This has all gotten so confusing.
You dropped your iPhone while it was in the Otterbox case. But you're asking if Apple will do anything. Yes, they will. A Genius will look at your phone. If you have Applecare+ the Genius will then sell you a new phone for $49. If you don't have Applecare+, the Genius will sell you a new phone for $199.
Neither Otterbox nor Apple make any promises that your phone won't get damaged if you drop it. A case MAY help protect it, but there's no guarantees. If you want to call Otterbox, go for it, but I doubt you'll get any help from them.
You dropped your iPhone while it was in the Otterbox case. But you're asking if Apple will do anything. Yes, they will. A Genius will look at your phone. If you have Applecare+ the Genius will then sell you a new phone for $49. If you don't have Applecare+, the Genius will sell you a new phone for $199.
Neither Otterbox nor Apple make any promises that your phone won't get damaged if you drop it. A case MAY help protect it, but there's no guarantees. If you want to call Otterbox, go for it, but I doubt you'll get any help from them.