Haste will decrease the time for DoTs, but will not diminish the duration, so basically it just ticks "faster". Because of that, you could get more ticks through haste.
From what they've officially come out and said, it's sounding like partial ticks will happen, where it'll tick, and then be active for 2 more seconds before falling off without a final tick, for example, just because of when/where the ticks lie on their timer.
This is what the theoretical soft-cap talk on DoTs is about: The point where haste gets you another tick, without wasting duration time.
Realistically, I'm seeing the haste generalizations on channeled spells falling over into DoTs.