From Pokémon Emerald onward, if a Pokémon with this Ability leads the party (even if fainted), the chances of finding a wild Pokémon holding an item increase from 50%/5% to 60%/20%.
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Whether Compound Eyes works in the Safari Zone is irrelevant to the question, as FRLG released before Emerald, which would mean Compound Eyes has no outside of battle effects in FRLG.
As for whether the ability works in the Safari Zone at all...
I went to area 3 where doduo is 15% encounter, caught 3 of them in 10 mins and two of them were holding sharp beak
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There's also this Gamefaqs post that discusses the topic for HGSS.
In an indirect way, yes. It increases the odds of an encountered Pokemon holding an item, but it does not increase the odds of finding a ~specific~ item. But since Compound Eyes will make it less likely the Pokemon will be holding nothing, in a way it does help you, since you'll have 50% more chances to find a Lucky Egg. Though in all honesty, I would jsut have a hacker/cloner trade you one, since it's only a 5% chance of finding a Lucky Egg.
You should also keep in mind that a Chansey has an at best 5.3% chance of appearing and a 5% chance of holding a Lucky Egg. That's a 0.265% chance of finding a Chansey holding a Lucky Egg, and that doesn't even factor how hard it is to catch...
Hope I helped, and if you have more questions please ask.
