Do maps with the Warbands mod generate more Warbands strongboxes?

I'm wondering if running Warbands maps improves the odds of finding one of the strongboxes required for the "Open a Unique Strongbox" challenge, since the strongboxes that count are all Warbands strongboxes. (My guess is that it does, but I somehow can't find confirmation anywhere.)

No. The Warbands boxes are just part of the normal game. The Warbands mod just adds Warbands to the map. Ambush or using Prophecies like Bountiful Traps or Monstrous Treasure are what you should do to increase the odds. Honestly though, you will spend more doing that than just paying for a box opening in Trade 820.