Would the ancient Dark spell that Wormtail carried out for Voldemort have still worked if Voldemort had not created Horcuxes?
On one hand, yes, in that no Horcruxes were used in the creation of the resurrection potion used by Voldemort at the end of Goblet of Fire to recreate his body. On the other hand, had Voldemort not created his Horcruxes, he would have been killed by his own Avada Kedavra curse when it rebounded from Harry and hit Voldemort when Voldemort tried to kill Harry when Harry was a baby. In that event, Voldemort would have been dead and the events at the end of Goblet of Fire would never have come to pass. So in this instance presumably no, because Voldemort would not have survived to get to the point of resurrecting his body. But the potion did not require a Horcrux to be created; if Voldemort somehow had managed to survive his first encounter with Harry, even though he had no Horcruxes, and had managed to make it all the way to the events of Goblet of Fire, then the potion should have worked exactly the same.
If we phrase that spell as a spell that took a surviving piece of Voldemort's soul and used it to reconstruct Voldemort, then it's essentially the restoring of a backup.
Had Voldemort never actually created any backups, there would have been nothing to restore, so it's not that the spell wouldn't have worked, but that no-one would've even tried to use it.
It would have still worked if his Horcruxes had all been destroyed.
The spell to restore the Dark Lord to a corporeal form was in no way dependent on the Horcruxes to work. (The potion to give him the creepy-baby body did use some venom from Nagini, but that didn’t seem to be related to her being a Horcrux.) When all his Horcruxes (plus the soul piece in Harry) were destroyed, he remained alive - until Harry killed him by reflecting his curse yet again.
He was already still alive at that point - the Horcruxes only work to tether the soul to life, they don’t restore the strength or body. If his Horcruxes were all destroyed when he created himself a new body, though, if his body was killed again he’d die.
But if he’d never made any, he’d just die - so couldn’t do the spell.
However, if the Dark Lord had never made any Horcruxes, and therefore never had anything anchoring him to life if he dies, he would simply die when the rebounding curse hit him. The only reason he was able to remain alive in a spectral form was because he had Horcruxes.
“My curse was deflected by the woman’s foolish sacrifice, and it rebounded upon me. Aaah … pain beyond pain, my friends; nothing could have prepared me for it. I was ripped from my body, I was less than spirit, less than the meanest ghost … but still, I was alive. What I was, even I do not know … I, who have gone further than anybody along the path that leads to immortality. You know my goal – to conquer death. And now, I was tested, and it appeared that one or more of my experiments had worked … for I had not been killed, though the curse should have done it.”
- Harry Potter and the Goblet of Fire, Chapter 33 (The Death Eaters)
His weak spectral form was directly a result of his Horcruxes keeping him tethered to life. If he had not created them, he’d never end up in that form - he could have become a ghost like Nearly Headless Nick but that specific “less than spirit” form was due to surviving death by use of Horcruxes. Slughorn had also mentioned that having a Horcrux would keep the wizard who had one alive but in an “inferior” form.
“Well, you split your soul, you see,’ said Slughorn, ‘and hide part of it in an object outside the body. Then, even if one’s body is attacked or destroyed, one cannot die, for part of the soul remains earthbound and undamaged. But, of course, existence in such a form …’
Slughorn’s face crumpled and Harry found himself remembering words he had heard nearly two years before.
‘I was ripped from my body, I was less than spirit, less than the meanest ghost … but still, I was alive.’
‘… few would want it, Tom, very few. Death would be preferable.”
- Harry Potter and the Half-Blood Prince, Chapter 23 (Horcruxes)
So, if he’d never created Horcruxes, he’d never have a use for the potion to restore his body, because he couldn’t lose it.