No. When you exit an app or press Home on your remote the app is effectively killed. When a screensaver runs, the current app may continue running in the background, although its execution is mostly suspended. Other than that, Roku devices can't run two apps at the same time. There's some system stuff (like checking for and maybe installing updates and downloading ads) that will happen while it's on the Home Screen and analyzing network traffic there's plenty of Netflix stuff that happens (Netflix has always been "special" and doesn't play by the same rules as other apps), but that's about it. That doesn't mean that a "System restart" once in a while isn't helpful like rebooting any computer and should be the first thing tried when having any kind of issue.
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