Would you consider a worldwide vote on if the character succeeds to be a tacky ending to a story? The means for the vote to occur are in place, but is it a satisfactory climax to have the protagonist win or lose because of public opinion?
Your protagonist needs to protag
My favorite definition for 'protagonist' is "the character whose actions move the story forward." A good test for a weak protagonist is one who spends the entire story reacting to the events around them, and never takes initiative for themselves.
Obviously the protagonist does not need to be responsible for every plot moving decision - villains and side characters get to have agency as well. But the protagonist should have more agency than any other character.
The place where this matters most of all is the climax. While all other points of the story can be carried by any number of characters, if you want your protagonist to feel like a protagonist, then they should be taking the initiative that navigates the climax.
Superficially, a world-wide vote is completely out of your protagonist's hands, and thus completely violates this principle.
That said, hope is not lost. If you draw a direct line between the protagonist's decisions and the results of the vote (for example, if the protagonist gave a worldwide speech moments before the vote, or if the protagonist's fame, earned through various earlier story actions, is a strong influencer of the vote), it doesn't matter that the vote itself isn't a direct protagonist action, it will still feel like a successful effort of the protagonist. But this can be a delicate line to walk, and you need to pay attention to your beta readers in order to see if you are successfully drawing the connection between the protagonist and the vote's success.
It is also possible to write a story where the main character is not the protagonist. In a case like this, a world-wide vote can be a good way of illustrating your character's lack of driving plot power. But such stories are more complex than average, and should be done deliberately rather than accidentally.
I would not do this. At all. This has been done several times in the past, and I don't recall any of them having a satisfactory feel about them.
One that still is spoken about in comic book circles is the death of Robin. Yes, one of Batman's Robin's fate was left to a telephone vote, and by a slim margin he was killed.
Your writing is your work, and it should not be left to anybody else.