By default, the HDMI output and the component outputs are live at the same time. The answer to your question depends on two different things:
1) Your input source- the 4306 will upscale RCA, s-video, and component signals to HDMI, but will not downscale HDMI to component. So if you want to use both the HDMI and the component outputs simultaneously, your input source has to be RCA, s-video, or component.
2) Make sure that you have analog to digital conversion turned on in the video setup menu. Otherwise, RCA, s-video, and component signals won't be upconverted to HDMI.
With those two things in mind, you should be all set.