No, the HDMI connector will just deliver the crappy picture that much better.
The whole point of using the composite connections, is apparently to soften or roll-off the video so you don't see the sharp/jagged edges.
Then, too, some TV sets handle the video processing differently on each type of input.
So, you can optimize the sharpness/brightness/contrast for the particular source (connector).
I watched a SD movie last night on my new LCD TV, and could see a little compression artifact, but only because I was looking for it.
Otherwise, it might have gone unnoticed by most viewers.
Don't forget that each channel is different on the quality supplied in SD.
Local channels are worst.
All the regular 'cable' channels are somewhat better.
The premium channels like HBO/ShowTime -may- be a bit better yet (or not)
With the statistical multiplexing Dish does (shares the bandwidth between all the channels on any given transponder) it's possible that any channel could take a momentary quality hit if all the other channels demand high data rate at the same time.