No, it doesn't. The drop chance is affected purely by the player. Specifically what equipment they are using. Equipment such as the Golden Serpent ring, and the Jester Hat boost item discovery, and there are consumables that can also boost your item discovery temporarily.
The best method for farming these is to equip your best equipment to boost your item discovery and start farming. Kill each enemy until they stop spawning, then use an Ascetic to boost the Bonfire Intensity, and make the enemies respawn.
However, it is possible that you can farm Titanite Slabs infinitely from the Stone Guards near the King's Gate Bonfire.
However, even with all of this there is no guarantee that you will get a drop, hence the term "chance". No matter how high the chance of getting what you want, there's always a chance that you won't, no matter how small.
EDIT: For reference, here is a list of all the locations, traders, mechanics, and enemies you can use to gain Titanite slabs. Remember, when you use a bonfire Ascetic, it will respawn items on corpses etc, but not chests.
 "Burning Bonfire Ascetic does not affect item discovery or drop lists."