It's a clever idea actually, kind of like the P2P network that torrents came up with. You don't handle the entire burden by yourself, but contribute to the network. Everyone does their own little part and it all adds up to one. If the network can support the assembly of data in a similar fashion to the way torrent downloading does, the speed can most certainly be fast.

But the cost effectiveness is questionable. Can you actually make enough to keep your laptop running nonstop day and night? How much would you be mining with this process? The same question for smartphones, even if the capabilities exist, are they worth the effort (at this stage)