I think you would need to test thousands of turns to make it useful. In one game with Order 3 Luck 3 I got treelord's staff, 2 clams, few more items, also vampire count, barbarians. All in less than 30 turns.
I don't want to test thousands of turns, but I did test (10 nations x 30 turns ==) 300. If you'd like to do more complete tests, go on!
I only tested the amount of gold and gems, and later items, you get with different scales. It seems that luck gives about as much gold and much more gems in the long run, if you manage to conquer as much as your Order neighbours.