PokéBase - Pokémon Q&A
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1 Answer

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Best answer

You should still be able to throw pokeballs but if it gets caught you will not be able to keep it.

The same thing happened in the first generation if a box got full - it didn't used to change boxes automatically. So if you caught a Pokemon you couldn't keep it.

But does it's data go to the pokedex
That's for you to find out :)