I play only 4-player games, and most are turn-based. I have hardly ever experienced someone leaving for no apparent reason. Timing out is even more rare as that only happens if the one of other players decides to kick you out for going over-time, and, since it's turn-based, nobody is all that uptight about it.
I actually find it happens more often in real-time games, that someone might flake, or have an issue where they can't stay at the game for the whole time, or takes too long and gets booted. Yes, involving more people increases the chances something like that will happen, but I don't like to play 2-player games, as I just can't get used to only being able to use one of the double tracks. So I play 4-player, but then again, I haven't had that much frustration due to drop-outs.
So yes, in my experience, in happens all the time that turn-based games are played to completion!