In the technical sense of the use of the word "authentic (sahih)", with respect to having a solid, complete chain of narration and solid textual sourcing, Du'a Sanamay Quraysh is not authentic.
(I say "technical sense" to specify what is meant because there are a lot of ways that people casually use the word "authentic" today.)
As for whether Imam 'Ali (A) actually said it... God knows best.
In any case, you have the option to recite it if it calls to you and you find benefit in it, and you have the option to leave it aside if you prefer to.