Do jailbroken apps on an iDevice remain after the device has been unjailbroken?

I'm considering jail breaking my iPhone 5 to play Pokèmon on it. Would child apps of Cydia stay on it, if I unjailbreak my device after getting the app?

And am I able to get an emulator on an iPhone without jail breaking it?

/facepalm…
you must literally not know what jailbreaking means if you are asking this question…

jailbreaking = install a custom bootrom to enable you to install non "apple certified" applications.

so if you are not jailbroken, you can't install non "apple certified" apps…

emulators are non "apple certified" apps, so obviously not…

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