So far the only official comment on luck I've found is a vague tweet about how luck increases the chances of getting higher rarity drops.
There are numerous conflicting comments and anecdotes on reddit as there always tend to be when RNG loot is involved. Some insist luck has zero impact on getting masterwork or legendary gear. Others insist their luck set consistently makes them get more masterwork items. Some are claiming they use to consistently get X drops over time with their luck sets but are no longer getting them since the patch (potential stealth nerf to drop rates or to luck affecting something it wasn't supposed to be).
This isn't something one person can really tell reliably on their own because it involves RNG. I've tested a luck set myself on my Colossus, but RNG is still RNG, so even if it's working sometimes I still get no drops in a run (besides the guaranteed drops from certain content on GM1) and sometimes I get multiples whether I have a luck set on with over 100% or none at all.
It really isn't something the developers should leave players in the dark about. Some people are using luck gear over larger upgrades because they believe it will result in getting more drops. If luck doesn't work on masterwork+ items, people should know. If a developer could clarify how this stat works more specifically and if and how it affects potential masterwork drops, that would be great.
There's also the question of how luck works in groups. Does it only affect your personal drops? Does the luck of the person who got a kill or opened a chest affect the drops for everyone? Does luck average out over the entire group when it affects drops (the way Diablo 3 splits bonus experience stats)? I've seen some players claim with enough luck you never get white drops anymore, but when trying farming with a set with 150ish luck, I still saw white drops occasionally.