Given how much free software is developed by volunteers across the planet, communicating almost entirely, if not entirely, over email, I don't see why a "distributed startup" couldn't work in theory.
I worked for about 18 months developing avionics networking software for a big company, and I worked almost entirely by myself in this country; most of my co-workers were in China. Even the people that I did communicate with locally, we usually spoke over email/IM.
As a maintainer for a GNU package, though, it seems that volunteers come and go, and their interest levels vary wildly. I think that the big problem with distributed startups wouldn't be, "can we actually develop a product this way?", but rather, people would feel more free to just up and leave the project, and never be heard from again, if there wasn't more of a social, in-person bond to the company.
This begs the question... could a startup be run as a quasi-volunteer project like GNU? Contributors would likely expect to be paid, either in cash or in equity, if the project is a commercial business venture, so that detail would have to be sorted out somehow or another. But it might be doable.