Can I use cards like Hand/Card Destruction while Thunder King Oh-Rai is on the field?

Well I've always wondered when you get more cards out of your draw phase considered either overall adding cards or drawing them, such as Hand Destruction, cards like that say you "draw" cards out of your card outside of your draw phase pretty much, when the card says draw does that apply to Thunder King Oh-Rai's permission to still being able to getting cards from your deck as long as they are "drawn" even outside the draw phase or is that adding cards?