Judging the picture on the right side of the screen on this link:
Solatube Daylighting Systems for homeowner projects are the smart alternative solution to traditional skylights
It looks like the tube reflects the light. I wouldn't think that a horizontal run would matter much. How long of a horizontal stretch are you talking about? Do you have the ability to run it through some sort of attic or access above the ceiling over the sunroom and living room? I just looked at the pictures you posted in your intro, and it looks like you do have some space between the ceiling and roof over both the sunroom and covered porch. I would go for it.
I have a ranch style house, so my installation would be be straight forward. I'm hoping to hear something from Sandy, to get an idea what you or I will be up against.
I will be home from Iraq on vacation again in Dec. My "plan" is to install them then. I say "plan" because you never know what the wife may have "planned" LOL!