Can I create a game where users can also play or interact with other users through a chat button or verse button. And by other users I mean any other player any where around the world?
I'd like to know this myself. I understand what you are asking. The closest thing that i can think of is Game Center unless someone else knows an other way.
You can not do that with GS. Not even with GameCenter as GS does not have the multilayer function. With GS you can only use Achievements and leaderboards.
There are other SDKs that could maybe integrate that feature like maybe: corona or stencyl but I think they are harder to use than GS and I don't even know if they have that feature.
Well I think it was being experimented on a few weeks ago about using URL links to send info by email or something which seemed interesting to see but never saw the results of it. But other then that no you can not as far as I know.
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But other then that no you can not as far as I know.