Subways don't come into HND so, even if you get this card, you'll still have to pay for some of the transport. Now, some of the Asakusa subway trains do run straight onto HND. But those are operated by Keikyu (non-subway). So I doubt that you'll be able to use this card on the Shinagawa-HND portion.

Looking at some prices here... if you decide to bus straight from NRT to HND first, then it's 3000 yen. Say you head to Shibuya after that, it'll be 560yen one-way via Keikyu to Shinagawa then Yamanote line. Alternatively, it'll be 740yen one-way via Monorail to Tennozu Isle then Saikyo line. Okay... I said earlier to take the Monorail via T.Isle to Saikyo line, but I didn't think it'd be so much more expensive going that route. So just do the Keikyu-to-Yamanote. In any case, NRT-(LimoBus)-HND-Shibuya-HND will cost you 4120yen total.