Version 2.0 of Elgato Game Capture HD software introduces a new feature called Stream Command.

Stream Command lets you add Webcam (Facecam) video, or an Image overlay, to your Live Streaming video.

You can find out more about Stream Command here:

How do I use Stream Command with Elgato Game Capture HD 2.0 software?

Windows: Webcam video can be used while streaming, and it can be saved along with a recording.

OS X:  While Webcam video can be used while streaming, that Webcam footage cannot be saved along with a recording at this time.

 

Saving Webcam Video Separately

If you create a Scene with Webcam (Facecam) video, and record it, you can later save that Webcam video as a separate video file.

To do this, Right-Click on the video timeline in the Edit section, and then select "Save Webcam Video Only".

You can also choose the "Export webcam to a separate video file" option in the Sharing section of the Preferences.  Then, that process will happen each time you share a recording.