The short answer is (very probably) no, it will not be rejected because of looking old. The long answer is: I have seen many app updates recently (since iOS 7 was released) which have very big mistakes regarding iOS 7 design, and some whose design has nothing to do with iOS 7. As an example, you may find Quickoffice with an update Sept.19 that has an older design (iOS<7 look).
So, within the long answer and based in my experience, your app will not get rejected because of having an old look, with highest probability.
It could still happen that your app got rejected though, since Apple's review process is a black box. You could then appeal to the Apple Review Board. If the app needs to have that appearance, they would accept it with high probability in case you argued correctly why your app needs that design (I also have experience about appealing to the review board and they tend to understand developers' concerns).