It will I think. Somehow I can see that twitter is just like following the things that facebook do. So I guess that it will do the same

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It is just not a question of Will facebook and twitter support and follow crypto currency , It is when they will start doing it. There will be no option for anyone whether it be social media or any business/shop to deny the option/importance of crypto currencies.
Still a big question as the fluctuations and sways still dominating the fear of most people who are gaining interest on this investment, twitter will welcome it when most people will do embrace the chain, the pressure will force them as digital currency will push thru and crypto will gain more supporters afterwards, just need some time.