Luck doesn't have any effect on the quality of drops, rather than in the amount of drops themselves.
I ran with only 7 luck through the entire two gameplays and I got good drops and some lame ones, hell I even got the Guillotine Axe from a soldier rather than from BP Miranda.
Sword of Searching does augment the quality of drops, but only for random Ores, so you can get let's say, better Hardstone drops, but the same Bladestone drops.
Current PC Build
CPU - i7 8700K 3.7 GHz (4.7 GHz turbo) 6 cores OC'd to 5.2 GHz with Watercooling (Hydro Series H110i) | MB - Gigabyte Z370 HD3P ATX | Gigabyte GTX 1080ti Gaming OC BLACK 11G (1657 MHz Boost Core / 11010 MHz Memory) | RAM - Corsair DIMM 32GB DDR4, 2400 MHz | PSU - Corsair CX650M (80+ Bronze) 650W | Audio - Asus Essence STX II 7.1 | Monitor - Samsung U28E590D 4K UHD, Freesync, 1 ms, 60 Hz, 28"
