In nearly every game i play someone disconnects at the very beginning. Is this caused by someone leaving the game already? I would find that very hard to believe because it just happens too often.
I had similar impression for some time,but it is really just the random luck of matchmaking.To most of them the problem is game crashing since on the beggining there is a bunch of things thath needs to be pre-loaded,depending on their PCs something is about to go wrong.
For some time there was a bug that would often crash the game when loading certain characters,it was weird too see almost all players disconnecting and I was wandering the same thing as you are...untill it crashed on me too.
Thing is that dota 2 is still in beta so the crashes and bugs are expected.Before the tournament developers tried to balance the game and make it more stable,and yet it was common to see players on tournament getting disconnected.Note that they were playing on same "network" and probably high-end mainteined computers,which is usually not the case with common players.