Are the spawn chunks loaded in Minecraft when you log out on a server?

Are the spawn chunks loaded in Minecraft when you log out on a server?

Added (1). I logged out of the world but the servers was still on. Do I have to be somewhere in the world for the chunks to be loaded? I made a chicken farm last night and logged out. When I logged back in there were no cooked chicken.

Chunks don't remain loaded when you're not in the server, if you have modded minecraft then you may have chunk loaders/world anchors which load chunks when not in the server. This can't be done on vanilla minecraft.