I'm not sure if there's any soundcard on the market right now with HDMI. It seems as though they've gone by the wayside. I'm in a similar boat- the PC is far away from my TV and in a closet and I want simulated surround sound on my Headphones (mainly for movies, not games).
What do you currently have your headphones connected to? The PC? A receiver?
I actually run HDMI out of my video card, with audio, to my den's receiver. I run the other HDMI out to a bedroom TV - the receiver in there doesn't have HDMI so I run optical out of the onboard sound. I do not experience latency.
Depending on how you intend to hook up your headphones, you wouldn't necessarily be running analogue cables. You could potentially run optical or coax out.
Note: I'm using an nvidia card (forget the exact model at the moment) and as far as passing along DSP effects - it works fine for movies/music using J River Media Center and various VSTs. Effects applied in other software also pass along fine. Obviously if you get a sound card with built in DSP like CMSS-3D or the like, I'm not sure how you would get it to take effect on your video card's hdmi/audio out. I don't think it works that way
Test driving a Xonar DG in the same box and I have to use one of its various audio outs to get the dolby headphone processing.