It's possible, with trading. I once went for a living dex, but soon realized that in doing that I wouldn't have enough space for Pokémon I like/special Pokémon/ breeding. I have at least one of most every evolution line, with major exceptions including event-only Pokémon such as Celebi, Victini, and Mew.
White 2 FC: 2624 0707 4433 One day, long ago, I ate a glowing piece of moldy cheese. Later that day, VeghEsther was born in my bathroom.
I have all 649 caught and in numerical order in their boxes in a living Pokedex that I have been transferring since Ruby/Sapphire. I don't have an AR either and every Pokemon I've got passes the tests for legitimacy.