Opera on iOS is actually Opera Mini, which doesn't run a rendering engine on the device at all. And no, Apple does not allow other rendering engines so much.

Opera on iOS is actually Opera Mini, which doesn't run a rendering engine on the device at all. And no, Apple does not allow other rendering engines so much. Specifically, they do not allow anything that can execute code that is not distributed with the app. So for example, no JS engine that's allowed to run scripts that don't ship with the app, period (even without a JIT).