...it's a game made in Japan. Which means japaneese people most certainly played it. Which means, that there is propably a whole club of people who caught every single one of these little f***ers...
It kinda depends on the definition of "caught" and "all". Every new generation adds some new pokemons, and you can't 'catch' some of them (starter pokemons, for example, can only be obtained at the begining of each game, and only one per playthrough). Considering the fact, that the only thing you have to do to get the 'caught' icon and additional data in the pokedex (at least in Ruby/Saphire/Emerald) is just HAVING that pokemon at some point in the past, you can theoretically get all of them by getting every single pokemon on his most basic level (sometimes more than one copy in case of pokemons with multiple evolution possibilities, like eevee), and then training the sh*t out of them (or using stones, or raising their happiness, or whathever) until they evolve. Of course, that would mean, that you've lost the original pokemons (unless you count evolutions as the pokemons they were before)...
I have no idea what I've just wrote, because I'm trying to do way too much stuff at once, so here's the short version: yes and no. It's very likely that there is someone with a full pokedex, but whenever he "caught them all" or not depends entirely on your definition of 'caught' and 'all'.
