For the latest version of the ArcGIS Runtime for iOS 10.2.3, the XCode 5/5.1 and iOS 7 SDK (or higher) are required to develop the application. Please check the System requirements for details.
For your question about using older iOS SDK such as 6.1 or any other iOS SDK lower than 7. You have to use older version of ArcGIS Runtime for iOS such as 10.1. You can find the older version of the ArcGIS Runtime for iOS SDK here: http://www.esri.com/apps/products/download/index.cfm