It would be almost impossible to fake the type and length of her cough bouts. She is not that talented.
OTOH, If this is real, then we'd have to believe that she coughs like this all of the time but has not gotten it treated, or she only coughs like this while giving public speeches. It certainly wouldn't be the biggest whopper she's ever told if I'm right.
And, actors could do this on a whim if the role called for it.
Unless and until something occurs to prove otherwise, I'm not going to take any stock in this.