Linking your chain to the spawn chunk is not necessary. You just need to make sure there are several items in each hopper and ensure you don't unload both chunks at once.

If you go out of range to unload only the furthest hopper, the closer hopper still in range will kickstart the furthest chunk and load it. When the closer chunk goes out of range the further one will do the same and keep both chunks loaded.

It won't work if you unload both hoppers at the same time, so if you chainload a large area it makes it much harder to unload all the chunks at once (unless you teleport out of the area)