Currently if you pin a PowerApp to home on your phone, the pinned app will give an error that the app didn't install correctly when you are offline. Even if you have downloaded the app and the app has offline capabilities. The pinned app will open up fine from withing the PowerApps app or when you are online.
Also, on iOS, when you use seach option to find the pinned app you can find it, bit you cannot open it bij selecting the search result.
Please update these behaviors to make the Pin to Home option better.