Man, I was getting all ready to get all lore-dork on the OP and then I actually realised that's /plausible/.
It'd be -absolutely hilarious- if the Garleans were, unwittingly or knowingly, using a Primal in their plans to fight the Primals.
And they did say Odin wouldn't be a Primal in the vein of Ifrit/Garuda/Leviathan/Titan, since they already had other plans for him...
Odin was (arguably) the single central NPC in the FFXI storyline, the single point tying the entire thing together. I've been -waiting- for him to appear in XIV, and... now you've really got me thinking.

(Other plausible inhabitants of Dalamud-as-a-prison: Ramuh, given the purple lightning bolts? I really like the idea of Dalamud as a prison the Empire is going to inadvertently unlock all over Eorzea.)