I'm using it now, and it's so close to being exactly what I need, with two necessary pivots that seem almost predestined to happen from your current position. The current basis of it being an inbox for files is already on the right track, and something I haven't seen attempted before, but it needs a little more verisimilitude to email:
1) The requirement to invite / induce signup / confirm "connections" needs to be ruthlessly optimized out — I should be able to just send a file to any email easily, forming a 'weak' connection. Maybe they have to do a 3 second signup to download the file, but it needs to be all in one motion. This obviously brings up a ton of issues like how to display the now 4 types of connections and unsolicited files, but it's essential to you getting traction.
2) 'sent' files need to behave like a outbox — remember that one of the biggest uses of email attachments is just sending stuff to yourself. Really you should just implement that straight up, it's the biggest use I'd have, and one I think you would find yourself as soon as you get the iOS client going. The dropbox iOS app's UI is terrible for it (pick one photo at a time and wait), plus really the filesystem metaphor is all wrong anyway! I actually want the transactional inbox feel of email here. If you don't explicitly support this I'm just going to end up using it with a computers account and an iPhone account.