That would have much the same cost effect if the server were kept up for it, and wouldn't be effective if the server were taken down.

It's been a while since I played minecraft, so I don't know what a chunk loader is.

When I played, if nobody was in the vicinity of the chunks with your farm in it it would unload and of course then the farm would not produce, so people would AFK in their farm to keep the chunks loaded.

Some Minecraft mods add items that force the game to keep certain chunks loaded. From the casual "Can't you just" I assume the parent meant those. It is however also possible, but much more complicated, to force the game to keep chunks loaded in Vanilla Minecraft. [0]

[0] https://www.youtube.com/watch?v=dx5Wd28AKxQ (the video is a couple years old so the current implementation might be different, but I think the basic principles are still the same).

ilmango dropped a new chunk loader a few weeks back - https://www.youtube.com/watch?v=B8z7q_pwjL4

Looks pretty easy to build.

If it's a mob farm, a chunk loader won't work on its own, I think?