Yes, you can upgrade the reports. However, you will not get any of the new features of CR 2013, such as the new export formats, when you run reports in your BO system, with or without the SDK. You would have to upgrade to BIP 4.x to get that. The latest version of the Crystal Reports SDK does NOT include support for connections to BusinessObjects and the latest version of the BusinessObjects SDK will not connect to BO 3.1.
-Dell