I'm no fan of the anime, but I can still say no, it's not gonna happen. The story writers know better than to put such a rigid structure on their series, considering that the show isn't based on manga.
Ash, or baka, as I call him, (lulz, Japanese for 'idiot') was never even close, and never will be, to catching them all. By the end of season one, when there was only a reasonable 151 to catch, he had about THIRTY Pokémon, that's not a very healthy ratio. And he seems to be catching less and less every generation now, whereas they just keep MAKING more every generation! So no Ash, if carching them was your real test, as the original theme song lyrics suggest, you failed hopelessly.
Hora kimi no sugu me no mae ni iru, sono namae wo saa, itte goran kono boku no namae wo! eFTo