I have dug a little further into the solution with recording from the Homerun directly to a NAS, and there are some issues; the system requirements for the Homerun is a Core 2 Duo cpu and 1GB of RAM, so most Synology NAS boxes will not be powerful enough. At least the ones intended for home use.
A Synology employee responded to my worries as follows:
A DS713+ will indeed be better. Or any DiskStation with a CPU which can transcode (DS412+...)
If you choose a DiskStation which cannot transcode, it's still possible to use the HD Homerun, but the streaming may not be as smooth, and when you use it from an iPad (through DS video), you will need to use have installed a 3rd party Player. This is because the format of the stream sent from the HD homerun (or any DTV tuner in general) is Mpeg2, which isn't played by the default player on the iPad (mp4, mov, m4v).
Also, your network will have just as much as influence as the CPU on the streaming smoothness.
As far as I have read the dual core CPU's in for example the 713+ should be able to transcode 720p video and some 1080 streams, so we are at the limit of the NAS' capabilities here.
My MacMini is vastly more powerful than such a NAS, while idle power is lower, the footprint and noise is similar. The Mini if more expensive, but not too much. The problem is that the SSynology setup and software works really well, and setting up a Mini as a dedicated will be much more trouble I suspect (and I will miss my Synology IOS apps...)
