Yes, they respawn eggs even if loot respawn is off
You know, it may be a small thing, but this is one of my favorite features of the mod. Loot respawn is necessary for MP but in my single games I always have it off. I think immersion adds so much more to a game, and finding new eggs from the chickens (and you see the eggs in the nest) while not having that bag of garbage magically have new things to find really makes it work. The mods immersion in general is great. Need some quick storage, just grab that empty cardboard box. Small things like that, but it makes it a favorite mod for me.