Syndra R and Deathfire Touch

So abilities like MF E and R, Rumble Q, Corki E, Garen E (late game) all apply damage in ticks faster than 0.5s, meaning they can get more DPS out of Deathfire Touch. Obviously you don't want to take deathfire touch on some of them, but that's beside the point.

Would each ball from Syndra's ult reapply deathfire touch? You're definitely getting hit by more than 2 a second. Again, whether or not deathfire touch is optimal is beside the point.