As far as I know, you do NEED them in your inventory. Dropped boxes count towards the big counter, but not your individual counter. Meaning you need to pick every single one if you want either the 400 for the universal prize, or aiming for top 10.
EDIT - for reference, I participated in the last event, Recette and Ana each got more or less 70k to 75k each, and I got some 10k to 20k from kind friends, for a total of 160k hunter boxes. If they counted immediately after dropped, then Recette would have been in the top 10 as well. Therefore, unless they changed something, the above answer stands.
Recette - Witch 400 | EmiriTachibana - Diva 400 | SakuraHiiragi - Champion 35x | AnaJessicaAyano - Soul Master 26x | LeslieSun - Witch 26x
Bye Bright Shadow Japan, I will miss you all and my bunch of characters very much ~~
Last edited by Recette; 03-14-2012 at 08:31 PM.