Mounted Canon VIXIA HF G20 -
As long as the HDMI output is configured properly, it should be the same as what is recorded.  I'm not sure about that particular model, but most higher end video cameras support clean HDMI or SDI output.  A clean output means it is free of any of the on screen displays.  They may also be capable of outputting different resolutions between the HDMI/SDI outputs and the recording.

As long as the HDMI output is configured to match the settings of the recording, then it should be the same signal.  Since it is digital, as long as the signal isn't dropping bits of data entirely, there won't be the traditional type of quality loss from analog transmissions, but you'll want to make sure the HDMI run isn't longer than necessary.