I have a Hauppauge HD PVR Gaming Edition (First Edition, green glow). I am not willing to buy another Capture device for the Xbox One alone.
I also have an Turtle Beach x31 Wireless Gaming Headset.

The HD PVR only allows component input on my 360 (no HDMI), so my current 360 set up is:

Xbox > Component Wires into HD PVR > Component into TV
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I know that I can buy a HDMI to Component converter that will convert the HDMI input to a Component output which will allow me to insert the Xbox One HDMI into the convert and also on the other end connect the component wires from the converter to the PVR to the TV.. Here is an example of the converter kit:
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(yes I have done my research, I know everything about the quality and stuff so don't mention things off-topic)

So then my set up will be like this for the One:
Xbox One HDMI > Converter > Component into HD PVR > Component into TV

So now my last thing that I was wondering is that... My X31 headset has a red and white RCA input which allow the Xbox Red and White composite/component cables to go into the headset RCA cables (Red and White). If you look at this picture, you will see there are two reds and two whites:
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So will I be able to hear game audio and chat audio on my xbox one from my X31 headset if I have my set up like below?
Xbox One HDMI into Converter > Component cables from Converter into HD PVR (WITH headset RCA Red & White wires into the back of the HD PVR) > Component output into TV

Would that above set up allow me to hear game and chat audio on my Xbox One?
If you still do not understand the Red and White headset wires, here is a video explaining it, the wires I am talking about start at 1:05 into the video. [ Register or Signin to view external links. ]