I've tried to hack together something like this but had trouble getting the initial torrent to seed from behind a NAT. After reading up on the BT protocol, my conclusion was that it really works best when you have a large swarm of peers. For sharing a file between my 2-3 devices or with 2-5 friends/coworkers, I want a protocol that works to establish the fastest connection between me and 1-2 other peers (taking advantage of local networks), not one that's designed to peer me with 15 other people. I'd encourage anyone interested in this to check out AeroFS.
Also, I think I had seen an earlier iteration of this that was using some kind of technique where they sucked the data you wanted to share into their seedbox. I wonder how they got around that.
One thing dropbox and other cloud-based sync providers have going for them is that they've solved peer-to-peer NAT fairly well.
I've always thought that the simplest way of solving the problem of "I want to sync an arbitrary amount of content between two computers, and I don't care that it's not available 'in the cloud' when all my machines are off" is to build a communication channel on top of dropbox (or something else). Although it's likely that Bad Things could start happening once your usage profile starts getting attention.
Also, I think I had seen an earlier iteration of this that was using some kind of technique where they sucked the data you wanted to share into their seedbox. I wonder how they got around that.