I once got Windows File Replication Service operating between my home network and the company where I worked, but I'm not sure if Home Server runs that service. I was a Windows nerd at the time, complete with rack, rack mounted servers and routers in my bedroom. Oh those were the days. [sigh]
Now I'm a complete Apple fan boy, and totally out of touch with Windows versions and what runs what. Plus I'm a total cloud convert, so I use AWS via JungleDisk for online backup, and archive to HDDs and DVDs back home in Australia for the data I don't need to keep online. I have the Apple Time Capsule for central in-home storage, and the 1TB is more than enough for my needs, and the automatic and centralised backup for the laptops is a dream.
What's missing to make my current setup ideal is a way to have the Time Capsule backup directly to AWS. At the moment I have to do it through JungleDisk, which is not very glamorous.
NAS is usually storage with a file system chip attached, and so isn't capable of having programs installed on it, *usually*. But they're coming out with all sorts of fancy devices these days. You might find one where you can install linux onto the device and access it remotely from your machine (no need for KVM). However, as it appears you've already discovered, there are plenty of tools which run on a local computer to access local NAS and backup to a remote location, usually via FTP/SFTP or RPC over HTTPS (i.e. VPN).
Boy I miss those TLAs.
