No, as scoop said Hard Mode "SHOULD" give you double drops at certain check points. Once you complete a phase in Hard Mode it registers in game that you completed it on normal as well. Only way to get multiple drops is to have multiple characters of the same class otherwise any armor drops will be locked to the class you completed the phase with. Perk to doing normal then hard is if you are hunting for a specific piece of armor or weapon that drops in normal mode because normal has a smaller loot table so technically your change of getting a particular item goes up. Then do Hard Mode for the larger loot table and hard mode specific items.