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Yes.

getcloak.com is a combination app and subscription VPN service that makes it easy. You can either switch it on, or set it to always on. You can decide which wi-fi networks (or cellular) to "trust" (exception to always-on).

The VPN, including always-on functionality, is implemented by iOS. The Cloak app merely configures it via API (or via configuration profiles prior to iOS 9).

F-Secure's FreedomeVPN is a great persistent VPN service that also runs anti-tracking and other security features. The iOS app runs great and always connects over VPN.

In android this is (was?) a built-in feature, no need to install profiles or apps. I say was because it seems like Google is removing all the things I liked about android.