Running component from satellite receiver to your audio receiver then running component to your TV should not significantly diminish video vs running HDMI from satellite receiver to TV. At larger screen sizes, you may see a difference. Also, HDMI can do 1080p, but component cannot.
You will not be able to switch video sources going to TV with your audio receiver's remote because the DVD player's video is connected by HDMI to your TV, bypassing your audio receiver. (You can of course switch audio sources at your audio receiver if you connect the DVD's audio and satellite's audio to the Sherwood.)
You do not need a DVD player with HDMI to be able to do upscaling from within the DVD player. Several DVD players can upconvert to 1080i/720p through component. A good example is the Momitsu DVD-V880-DX; this player will also disable Macrovision copyright protection from a secret menu. Upscaled picture to 1080i/720p by component on Momitsu is very close to upscaled picture to 1080i/720p by HDMI on my OPPO on a 102" screen.
If it is really important to you to be able to do video switching from the audio receiver, then you can connect both your satellite receiver and your DVD player to your Sherwood with component cables.
My personal choice would be to keep the switcher and use HDMI for both sources. I am somewhat surprised that Sherwood costs $2000 and only upscales from composite and S-video to component. You can get HDMI switching in a receiver these days at half that cost.
