It would not, as it is now, your Draw draws your card, then goes on cooldown. Then you either use Play to throw the card at someone, Redraw it for a new card, or Press Minor Arcana, get a Lord/Lady, then you have to press Play again to play the Lord or Lady card.
Now it will be "Press Minor Arcana, and it automatically turns into and plays the new card." They essentially now cut out the middle man and play it the moment you convert it. Draw will always go on cooldown, so you are not delaying the draw cooldown unless you simply do not play the card within 30 seconds (at which point the Draw is back off cooldown"