No, but you can hollow it out using the chuck on the drive side before shaping and use a boring gouge from the rotating center, then a drill attachment with Forstner and or spade drill bits. I’ll try to make a tutorial using these or come down when you’re doing this.
This is interesting! I’d been thinking of like a salt mill to match a pepper mill that I inherited. I wasn’t sure if one could buy the mechanical parts though.