This is certainly how it works on iOS but it could be realtime except, I assume Apple's motivations for not doing this is for experience immediacy e.g. if the user wants to open a new app, any old app could be flushed from RAM immediately. That said, UIKIt does this for he UI if the system terminates your app. The inconsistency is Apple's.
What I was really referring too was the concept of clearly defined save state and API to allow near seemless suspemd/resume. This does require a little effort as not all iOS apps support this. But on a device primarily designed for playing and switching games, I'd expect Sony to not make the same compromises as Apple.