Linux, can a home directory be symlinked?

What you describe is one strategy that will work.

Another would be mounting the drive at /home directly, instead of at /media/storage. If you did this you'd probably want to move any existing data into other folders so you don't end up with extra /home/foo subdirectories.

The main potential problem with both strategies is that no home directories will be available if mounting the storage drive fails for some reason. If that happens, the symlink strategy will probably fail harder; the direct-mount strategy will leave an actual directory, so programs that attempt to access /home/foo will fail, but simply accessing /home will still succeed.

Instead of symlinking the whole /home dir to someplace else (say /media/storage/home), create symlinks for every user separately and leave your admin account unlinked so admin can always login

/home/admin is /home/admin

/home/billy is linked to /media/storage/home/billy