The HDHomeRun works very well with Myth. That's how my system here works and it performs pretty much flawlessly (at least since I diagnosed and replaced a faulty network switch that was dropping packets at random, but not enough to cause a complete failure).
I do know you won't be able to play HD content with the original Xbox, though. I have Xebian on my original Xbox and tried using it as a Myth front-end for a while but it just doesn't have the horsepower for anything over DVD resolution.
I don't know about using dual-core Atom - if you meant just for the back end, that should be fine. If you want to play back HD content, I'm not so sure. My Atom-based netbook seems to do OK (just barely) with down-scaled (to the netbook's native 1024x600 resolution) HD, but I've never tried it with a bigger external monitor. It is presumably having to do the decoding and scaling before it displays the content and it does keep up most of the time. I seem to remember it stuttering a bit on high bit-rate streams. I can't really remember much, though, as I don't really use my netbook as a Myth front-end very much.
I have no idea what DLNA is, so I can't speak to that.