No, Scale Dice do not add to Assets.
Assets are a single, flat calculated value; you don't roll any dice to determine Assets. Please see the formulas on the Asset Master Table on page 185; there are no die rolls listed.
The main thing Scale Dice would add to is HTH Damage from BOD (pg 91), and Standard Damage from Powers (pg 138). Damage is the most common and important Effect Roll.
Hope that helps!