If I buy an unlocked Apple iPhone5 online in America will it work in Ireland?

I was wondering if I got my cousin in America to order an Apple iPhone 5 online from the Apple store & it was delivered to him in America, then shipped to me, would it be fully functional in Ireland? Because it says when you buy one online that they are unlocked? Reply As soon as possible, thanks!

Added (1). I would just be worried that the App Store wouldn't work? Also would I have to jailbreak the phone for it to work?

Yes, thats the whole purpose of it being unlocked.

I have an unlocked and live outside US

Yes it would work fine.

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