Chucky is supernatural, they could if they really wanted to fit him into the game. While he prefers to hunt you down using his cunning yet comical ways he has access to some powerful stuff.
Chucky lorewise is as strong as a full grown man, he can easily drag a survivor instead of carrying them if the animation of carrying is too difficult to do. As for hooking them as we’ve seen in Cult he can can posses people into putting themselves on the hook by taking over their bodies, ala the way he was able to make Nica walk, Chuky also has a lot of voodoo lore (its the whole reason for him being a doll in the first place and how he keeps coming back lol) they could easily adjust the story of the Heart of Damballa to suit their needs for his powers.
Plus Chucky would come with the benefit of being able to get Tifanny or Shitface (lets not hto) as a model and voice swap. There’s no reason they can’t do Chucky aside from his carrying animation and pallet interactions (which they can just make him immune to it or crawl under it).
Saw puppet isn’t alive its just a puppet that John uses to send his voice recordings lol. Never going to happen.