Would it? Is there any country whose leaders are so foppish as to believe what they read on Twitter as though it were some actual diplomatic channel, or even an early warning system?
I'd wager you're correct in your assumption that most decision makers would not be duped by something like that, however a bogus tweet from an official source could be used as plausible cover for leaders who are seeking justification to take actions they wanted to take anyway.
Can you imagine what would have happened if a post-9/11 Iranian leader's account had tweeted "we have successfully acquired nuclear weapons and will be attacking Washington DC and Jerusalem tonight"? Elements within the governments of the USA and Israel have been agitating for war with Iran for decades, and that could give them the cover they need to act on it.
Color me skeptical, sir.