I tested it, and here are the results:
With every single consumable emptied: I looted in El Patron's Mine at the South Idol with a sword for six hours on Andaba. After doing so, I had exactly 22 loot skull chests. In those, almost every single one of them contained 2 or 3 of the slots filled with my lost consumables. Also, any time a consumable was completely refilled, I emptied it. However, I did obtain the following items:
- 3 Famed Items (Swamp Throwing Knives, Masterwork Cutlass, Divine Sabre)
- 6 Rare Items (Meaningless crap)
- 5 Brights (including yellow, orange, and other terrible ones).
With every single consumable full: I looted in El Patron's Mine at the South Idol with a sword for six hours on Andaba. After doing so, I had exactly 19 loot skull chests. In those, I had an additional 2 or 3 slots that were filling with loot rather than consumables. I obtained the following items:
- 1 Legendary Item (Lost Sword of El Patron)
- 4 Famed Items (Brigadier's Broadsword, Seven Seas, Golden Idol, and War Scattergun)
- 8 Rare Items (Meaningless Crap + Carrion Doll)
- 16 Brights (including yellow, orange, and other terrible ones).
That is my analysis, so I concur that HAVING FULL CONSUMABLES INCREASES LOOT CHANCES.