The very short answer is that we don't know. The most obvious change (that Cedric killed Neville at the Battle of Hogwarts) doesn't seem to have any bearing since that change occurred after Snape's death in the primary timeline.
What could have changed?
- Harry was deeply affected by Cedric's death. Although he suffered flashbacks and nightmares in the short term, Cedric dying appears to have steeled his resolve to attack Voldemort.
Harry watched Dumbledore striding up and down in front of him, and
thought. He thought of his mother, his father and Sirius. He thought
of Cedric Diggory. He thought of all the terrible deeds he knew Lord
Voldemort had done. A flame seemed to leap inside his chest, searing
‘I’d want him finished,’ said Harry quietly. ‘And I’d want to do it.’
Harry Potter and the Half-Blood Prince - — CHAPTER TWENTY-THREE — Horcruxes
- Harry and Cho were able to have a (brief) relationship now that Cedric was out of the picture. It's really not clear how this could have had consequences for Snape, but we do know that Cedric's death was a key reason for her joining Dumbledore's Army. With Cedric alive but humiliated, it's reasonable to assume that neither he, nor Cho joined up to fight Voldemort.
Well, they’ve forbidden me to get on the wrong side of Umbridge, too,’ said Cho, drawing herself up proudly. ‘But if they think I’m not going to fight You-Know-Who after what happened to Cedric –’
Harry Potter and the Order of the Phoenix -CHAPTER TWELVE - Professor Umbridge
- Dumbledore's Army was founded from people who'd turned up to hear the story of Voldemort's return and Cedric's death. His corpse was quite literally the only proof he had that anything untoward had happened in the maze. Without it, his story could be dismissed as a fantasy or an hallucination. Critically, without Cedric dying, fewer people would have turned up and hence Harry's militia would have been substantially smaller.
It had just dawned on him why there were so many people there. He
thought Hermione should have seen this coming. Some of these people –
maybe even most of them – had turned up in the hopes of hearing
Harry’s story firsthand.
Zacharias said dismissively, ‘All Dumbledore told us last year was
that Cedric Diggory got killed by You-Know-Who and that you brought
Diggory’s body back to Hogwarts. He didn’t give us details, he didn’t
tell us exactly how Diggory got murdered, I think we’d all like to
Harry Potter and the Order of the Phoenix — CHAPTER SIXTEEN — In the Hog’s Head
Which all leads to....
With a smaller army, with Harry less certain of his resolve and with the Death Eaters having a new and highly talented recruit, it's plausible that Harry was killed early enough in the assault on Hogwarts castle that Voldemort never felt the need to kill Snape.