Apple's capricious app store review policy aside, iOS is so locked down that even a completely malicious sideloaded* iOS app can't dig itself into the system like this. Without a local privilege escalation exploit there's just no way to set up a persistent background service and no way to escape the sandboxing to allow an app to leave a mark on the system after your app is uninstalled.

(*a developer can basically sideload any app on their iOS device with an Apple developer license)