unlikely. Torrents are slower, in most scenarios, than straight HTTP. With small files, they generate more traffic for chatting/handshaking than the file is actually worth.
It could however lower costs for people who distribute large files, where the final user can tolerate some download latency. I'm thinking browser games that can download a big archive via torrent on first launch, similarly to what Steam does now in their client.
A large majority of web clients must be operating on battery now, too. Willingness to burn battery participating in Torrent and other distributed protocols rather than HTTP will be low among those, let alone willingness to leave such a thing operating as a daemon in the background. It’s why I don’t see much future for these things (distributed file-sharing protocols) except in infrastructure or in applications where many users may be expected to be on desktop.
It would help lessen the cost of bandwidth for servers and smaller ISPs, as traffic is very expensive for anyone that isn't Comcast: saturating a 1 Gigabit line can cost an ISP ~$1K/month!
It could however lower costs for people who distribute large files, where the final user can tolerate some download latency. I'm thinking browser games that can download a big archive via torrent on first launch, similarly to what Steam does now in their client.