if I restrict internet access to an app that requires internet access, does that an essentially kill the app?

Not exactly. You are preventing the app from making any network connections. Some apps will continue to harvest data in the background or waiting for that opportunity. Once it connects, it will upload this data. 

But you can also do this manually presently by force stopping apps and ensuring sensitive permissions such as location or access to your mic or content are turned off manually.

We are working on this feature to prevent or limit this background activity and automatically toggle permissions in the foreground.