Yes, they do. What Bulbapedia says (I am supposing about the Pokemon Feeder):
In Pokémon Ruby, Sapphire, and Emerald, there are Pokéblock feeders throughout the Safari Zone. If a Pokéblock is placed in a feeder, all wild Pokémon encountered in grass patches and water tiles up to five steps away from the feeder will have a Nature such that, if an identically flavored Pokéblock were thrown at it, the Pokémon would be enthralled (i.e. its preferred flavor dominates its disliked flavor in the Pokéblock); the feeder has no effect if no such Nature exists. Only one Pokéblock may occupy a feeder, and the feeder's effect disappears after 100 steps are taken.
Also, throwing PokeBlocks in a encounter decreases the chance of escaping.
Throwing a Pokéblock that the Pokémon completely ignores does not directly affect the escape factor, but does increment the Pokéblock counter used for subsequent Pokéblock throws. A Pokémon is enthralled by a Pokéblock if its preferred flavor dominates its disliked flavor, while a Pokémon completely ignores it if its disliked flavor dominates its preferred flavor. If both preferred and disliked flavors are equal (including if neither are present), the Pokémon is curious about the Pokéblock.
Which messages about that:
Action Catch Factor Escape Factor
Throwing a Pokéblock the first time, and the Pokémon is enthralled, No change, Decrease by 5
Throwing a Pokéblock the second time, and the Pokémon is enthralled, No change, Decrease by 3
Throwing a Pokéblock each subsequent time, and the Pokémon is enthralled, No change, Decrease by 2
Throwing a Pokéblock the first time, and the Pokémon is curious, No change, Decrease by 3
Throwing a Pokéblock the second time, and the Pokémon is curious, No change, Decrease by 2
Throwing a Pokéblock each subsequent time, and the Pokémon is curious, No change, Decrease by 1
Source
Hope this helps!
