Yeah there appears to be a few bugs in the game including that. One bug is when you destroy one of those elemental charmers, the effect should not activate because effect is done after damage calculation, like how Black Cat with White Tail can't return itself if destroyed, but in the game the charmers temporarily take control of it and back.
You indeed cannot activate draw effects if there aren't enough cards in your deck PRIOR to activation. Furthermore, only being unable to draw during your normal draw phase leads to defeat.
To elaborate on above idiot comments. this card adds the three selected cards to your deck and then draws, so yes you should be able to use this if there is 1 or 0 cards left in your deck. however If you are planning to win by battle, then obviously don't activate this on last turn unless your opponent has more cards in their deck than you. otherwise this won't allow you to attack to win.
it probably has something to do with this card being able to return Extra Deck monsters to the Extra Deck (which means your Main Deck will remain empty, so the draw part cannot resolve)
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This. But the main problem with this card is, that you can target extra deck monsters. So it's possible that you would target 3 extra deck monsters and then you wouldn't be able to draw 2 cards anymore. This makes it impossible to activate when your deck has less than 2 cards.