Which is the point of Asynchronous play. I send you my play before I go to bed, when I get up I receive your turn. I get my next turn done during lunch and then perhaps you get it back to me right after I get off of work. We don't have to be able to play at the same time. But yes, this is a game that would take a couple of days by itself so you wouldn't be able to run an entire Tournament this way.
I know that, my point was just demonstrating why you shouldn't only have a tournament that is the conventional 2-3 days.
As this game does not have a huge player base yet and majority of them are scattered across the globe.