I just found out that in the battling eevee brothers James is holding a lobster to eat. So they definitely have some real animals that they eat
Kanto tended to play a bit looser with that detail, though. Real animal sightings/references were more rampant then, partly because they were still figuring out the rules of the Pokemon world, and also because they had a much more limited variety of pokemon to fill the relevant niches.
Anyway, here's Farfetch'd's original pokedex entry:
"Farfetch'd, a Wild Duck Pokémon. Farfetch'd makes a delicious meal, especially when cooked with leek. Because of this, Farfetch'd is nearly extinct."
I find it grim that Dexter actually emphasises that Farfetch'd is "delicious". It makes it sound like a recommendation. For an endangered species too!