[OP13-102] - Edison (Carrying On His Will)

If the number of my Life cards is more than the number of my opponent's Life cards, can I still use this [Activate: Main] effect to rest up to 1 of my opponent's Characters with a cost of 3 or less?

No, you cannot. In this case, you are both unable to draw 1 card and unable to rest up to 1 of your opponent's Characters with a cost of 3 or less.