The iPad does not have a full multitasking environment, in the sense that you can run two or more apps simultaneously. That means you can not run Google Hangouts and another app at the same time. So, no live screen sharing.
When you swap back and forth between apps on the iPad, the background app (with a few exceptions) is frozen in RAM, waiting to continue from where you left off, but not taking up any computing resources in the meantime.
The best way to share an iPad screen in Google Hangouts is to use an app like Reflector on your computer. It lets you use AirPlay to mirror the iPad's screen to a window on the computer. You can then share that window in the usual manner with Google Hangouts on the computer.
Good luck.