Bitcoin has already become a global currency, It did this when it was trading on the Stock markets, yes as a stock, but also as a currency if you look at the stock exchange you have all currencies traded, and then the commodities market is also Bitcoin. so it is in all levels of trade, and currency exchanges, this is what keeps it strong, and will make it stronger for days to come.
But in theory, it's also a global currency for being accepted as a payment from stores all over the worls. Wheareas for them to accept a FIAT currency from a certain country, they'd have to use third party services to convert them to their currency of preference. Thing is though, it's value is still based on FIAT currency and that's unlikely to change.