yes. They would have to dramatically decrease their bandwidth charges, and they'd have to lower their charges in general (just 'cause the barrier to entry for their competition would be lower) but if anything, having a fat pipe at home would make storing things remotely a lot more attractive.
Think about it; with that kind of a pipe, you could boot your desktop off of a drive in my datacenter, two cities away.
Think about services like OnLive (who even offers Windows in the cloud). We have these today, but if we had fiber everywhere, we likely wouldn't have the dvd drive in the Xbox 360. We certainly wouldn't need BluRay.
Think about it; with that kind of a pipe, you could boot your desktop off of a drive in my datacenter, two cities away.