Can I still download games on an unlocked iPhone 4?

I'm buying an unlocked iPhone 4 because I will be using it when I travel to Mexico. Which I do it often. Would I still be able to download games? Like can I plug in the iPhone to my computer and download games from the apple store?

Of course yes

An unlocked iPhone works the same as a locked one, except that it can be used on any GSM carrier in the world.

Yes. An unlocked iPhone works anywhere, but it's more expensive than a locked one.
i think you can buy a locked iPhone and unlock it through unlocker websites. My friend used 1 of them for unlocking his iphone for just $25 in 12 hours. They are official apple unlocker.
take a look at their website:
http://officialappleunlocker.com/

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