Answer:
Hello, Gary,
Yes, on those specific components (Sony BDP-S350 Blu-ray player and DISH Network ViP722 DVR), the component video and HDMI audio/video outputs are both active at the same time, so you can plug in your devices to the receiver via HDMI and to the TV via component video. You can still get high definition output from these devices (1080i) over component video, but the signal over HDMI can be up to 1080p. Also, the Blu-ray player will only upconvert standard DVDs over the HDMI connection (not over component video) so results may be better when you route everything through the receiver.
Keep in mind that, for the TV to get sound from these devices, you will also need to connect the left/right analog audio outputs from the Blu-ray player and satellite box to the TV's component 1 and component 2 A/V jacks. Otherwise you will get no sound from the TV speakers. This does make the connections a little more complicated but it will allow you to watch your programs and movies directly through the TV's speakers when you don't want to fire up the home theater system.
Hope that helps,
-Chris