App center for Worklight 6.1 works fine on emulator but on real device, after the splash screen, it gets stuck on a white screen.
Maybe are you using a Windows Phone 8.0 emulator and a Windows Phone 8.1 real device?
There is a known issue with Cordova on WP 8.1 which leads to this white screen issue: https://issues.apache.org/jira/browse/CB-6763
This issue should be soon fixed as Cordova 3.6.0 will soon be released.
Concerning your question about wether it is necessary to code-sign the application to run it on a real device... If you debug it from you Visual Studio project and choose a real device instead of an emulator, it will get installed on your physical device without being code-signed. However, this unsigned version of IBM Application Center will not be able to identify properly which apps from the Application Center catalog are installed or not. Using this is often suitable for developing, but for the final test phase or the production use, you have to get a code-signing certificate, and code-sign your Application Center XAP file as well as all the apps you want to provide in the catalog with this XAP file. You of course will also have to enroll your device using the corresponding enrolment token before being able to install any code-signed XAP on the device.
This is the only way to test that your Application Center mobile client is running as expected.