Courier is important. Otherwise you are forced to go back healing/getting items. Which will lose you XP and gold and ultimateley the game.
Yes there is Turbo, no it's not comparable to regular gameplay.
Regular dota players learn to play without the courier anyway, because someone always feeds it away or uses it to ferry themselves a magic stick.
So maybe playing without a courier at all would be more representative of the pub experience ;)
Courier isn't that important. It's being phased out across the recant patches. And there is a popular Dota mod with 5 fast invulnerable couriers.