If your question is,
Do Global Moderators have the global moderator badge, then yes, yes they do.
As outlined here https://help.twitch.tv/customer/portal/articles/659115-chat-icons-and-emoticons
If your question is,
Do Global Moderators have the global moderator badge, then yes, yes they do.
As outlined here https://help.twitch.tv/customer/portal/articles/659115-chat-icons-and-emoticons