simultaneous output

I want to connect my apple tv to my HDTV with an HDMI cable and then use component cables to connect my apple tv to a slingbox. Would that work? would I be able to sling and watch at the same time, or at the very least, when the tv is on will it go over hdmi, and then when I turn the tv off will it go over component? Or would I have to actually unplug the hdmi caple for the component cable to work?

Thanks!