See I never liked the timeline in the Cursed Child where Voldemort won, and not just because the Death Eaters won in that timeline. No the reason I don't like is because that timeline could not exist, and not because of the insult to Cedric's character, though I will mention that.
First the basis of Voldemort winning is because Death Eater Cedric killed Neville so Neville didn't kill Nagini and Voldemort won. Except that would not have happened if nevill had been killed. One, because there were plenty of other wizards and witches that could have stepped in and killed a snake with a sword, it was important for his character but it wasn't like he was the only one able to kill a snake with a magic sword.
Second, Harry Potter's protection made it impossible for Voldemort to hurt anyone there and Voldemort's forces were losing near the end, Bellatrix was dead, Dolohov was defeated, Rockwood was beaten, so was Macnair and the Lestrange brothers. So had Death Eater Cedric killed Neville it's not like the Dark Lord could have beaten Shacklebolt, McGonical, Flitwick, Molly, and several other powerful wizards.
Thirdly, Harry was the master of the Elder Wand so Voldemort couldn't kill him with that, even if for some reason they could kill Nagini the killing curse would have still rebounded on Voldemort from the Elder Wand and he would have been reduced to the same state he had been in Book 1, except even weaker with all those Horcruxs destroyed.
Fourth on Death Eater Cedric I think it is an insult to his character to think he would turn Death Eater because of some schoolyard embarrassment, Harry himself says how great a wizard Cedric was. If that actually happens he probably would have just laughed it off as something weird and embarrassing.