I was researching this same thing a few weeks ago. What I found was NO... building codes say not to run low voltage [HDMI- audio video wires] in the same conduit or same holes through the studs or within the same junction boxes with 120v or 220v power.
There shouldn't be any problems with HDMI and power next to each other as HDMI cables are shielded. Someone said if it was a big deal then why does the TV and the power cord connector so close on the TV, made sense to me and I could not find anyone who had any proof of any picture problems running them next together for less than 30 feet anyway.
I also found code does not allow for the TV power cord to gon inside conduit within the wall either. The safe way for power in the wall, I found the Powerbridge kit here and was really easy to install retrofit. Came with everything I needed and ordered the ROMEX as well. I actually bought 2, one for the TV and my subwoofer so they could be plugged into my surge protector.
Another post here had a link for $39.95 for AVS members, last I checked it was still good, although it did say for a limited time 2 weeks ago. http://www.powerbridgesolution.com/avsspecialorder.html
Good luck, just don't run the power cord in that conduit, could be a problem down the road.
The powerbridge is a decent option but I got a recessed outlet with scoop for less than $20 at monoprice turned around got thier in wall HDMI 1.3 cable for another $20 and I am still twenty ahead of the power bridge. If you do run the power and HDMI in the same conduit I would HIGHLY recommend the shielded in wall HDMI cable from monoprice. It is a beast of a cable and worth it.
The powerbridge isn't just "A decent option," it's the law. It is illegal / against code to run a device power cord (or a normal extension cord) through your walls 99% of the time, even if it's in conduit. You use the powerbridge or something similar because you care about legality and safety, not because it's the cheapest way to do it.
I would recommend against it. I just re-did my living room and did a LOT of research and here is what I came up with:
1.) Power - A separate romex cable that went directly to the electrical panel. The outlet fixture has a built in power surge protector. When I installed mine, they didn't make a recessed one, but they do now.
2.) Conduit - I couldn't find any (good) flexible PVC piping so I used some industrial type found at an electrical warehouse. I ran one large conduit for the HDMI cables, and another one for future cabling. I'm glad I did because now I think I have to add an optical audio cable and IR remote extender cable.
The construction may not look the cleanest, but the finished look is fantastic and everyone comments how nice it looks. If someone can host images, I can email them to you.