When the player's inventory is full / nearly full and only a partial stack is picked up from the ground (e.g. the player has room for 16 oak and there's a single Entity Item of 64 oak, only 16 will be picked up and the other 48 will remain on the ground) two things happen:
1) None of the "item picked up" effects play (the stack does not animate into the player, no "pop" sound
2) Statistics about blocks picked up are not updated