Well, I tested it by myself today.
I put backpack with assigned loot containers into the Depo (let me call it "main backpack"), then put imbued backpack into my backpack slot, and finally put "main backpack" into imbued backpack. Sounds complicated, but it's really easy.
Then I took of imbued backpack with the main backpack inside and put in one of my Depo chests. Put my main backpack in the backpack slot and imbued backpack stayed in Depo chest.
I had no problems with any mess and loot managments.