My instinct is to isolate data and power in separate conduits - it's "good practice" that is also very important with analog signals (both audio and video). I don't know if there would be a problem with HDMI's digital signal if it were run parallel to a power cord like this, though. Hullguy? Anybody else?

You could always bundle the two together outside the conduit for a brief test before you conceal them, especially since it's a short run and you could do it pretty readily before pulling them into the conduit.