Yes. I'm assuming you're wanting a 1080p final output... if you're working with a different resolution, just scale as necessary.
Increase your canvas size to 3840x1080. Set your normal capture scene up as you normally would (game capture, with small webcam on top), except put this in the left 1920x1080 area. Then just add your full-frame webcam source again, and move it to the right 1920x1080 area.
You'll be recording a 3840x1080 video, which is an interim for when you go to edit.
In your editor, you just need to add the recording twice, with separate crops - the left area for your main capture, and the right area for your full-frame webcam cuts.