Wouldn't it be the same end result because of the "do as much as you can" principle? You cannot target the hand for the underdeck, so 0 cards were underdecked, and the draw ability fires with the 0 amount. It's not a cost benefit, it's a related but additional ability, so I don't see any reason why it wouldn't trigger even if the first ability fizzles.
I mean I guess either way could work, but I think it's clearer/simpler to have it default to "0" rather than "null."
If the opponent has Music Leader and Hezekiah's Signet Ring (for some reason) and I play a mandatory search that targets draw or discard I don't get to search because HSR restricts me but since it's mandatory it still fires and I've still "used" the ability haven't I? It really depends on the definition of "using an ability", whether it's simply triggering the ability even if it fizzles for various reasons or whether the ability has to successfully carry out some sort of effect.