Somewhat yes and no.
>Many core series games feature other Trainers named Youngster Joey. However, these Trainers do not use Rattata and have no other connection to the Youngster Joey in Johto. Only the ones in Pokémon Black and White and Pokémon X and Y have the same Japanese name as this Joey.
There you have it. There's only one original Youngster Joey, the rest are all for namesake. They may not even have a Rattata.
Source (Bulbapedia has all sorts of stuff)
Hope I helped!