I have an update for everyone on this topic. I've had a little success thanks to previous posts.
For reference I am using an iPad 2 operating on iOS 6.## I have no clue if iOS 7 and/or newer iPads would make a difference, but from my research, I think not. I am using the most up to date Dish Apps.
When using my iPad to Composite cable, I am not able to play ANY of my dish content on to my TV (as previously discussed in the original post). This cable is great for non-HD TV's when wanting to pipe a movie or any other app (Netflix or Vudu for instance) on to the TV. This cable does NOT do iPad mirroring.
I picked up an iPad Digital AV Cable. With this cable, my iPad supports "mirroring" on to a HDTV. With this feature, I AM able to utilize the Dish Anywhere app to watch DVR or Live TV content via the mirroring feature. However, the Dish Hopper Transfer App doesn't work. When I try to play a show when my iPad is mirrored with a TV, the app comes up with a message to the effect of "this app does not support mirrored play feature". It was an app pop-up window, and NOT an ipad one, thus it is clear that this was a conscious block up in place by Dish. For me, however, this wasn't a big deal.
The larger "problem" however, is when watching Live or DVR TV via the Dish Anywhere app via a Mirrored setup with the Digital AV Cable. Because an HD TV is wide screen (for simplicity we will say 16:9), and an iPad is closer to standard screen (again for simplicity we will say 4:3), the iPad mirrored screen displays as 4:3 on my 16:9 TV. In other words, big black bars on the left and right. Then when I watch a TV show via the mirrored setup, because the show was recorded in say 16:9, on my iPad, it tries to play the 16:9 show on a 4:3, thus putting black bars at the top and bottom. When you then add in the mirrored setup I now have black bars on left/right AND top/bottom. This in essence turns my 52" HDTV in to a say 42" HDTV. This kinda sucks, and I personally fine the black box around the show a bit distracting. Thankfully the TV I'm doing this on has a "zoom" feature. This is pretty successful in getting rid of most of the black bars around the video, however, it is at a cost of resolution/quality. The video quality does drop when zoomed. I imagine this is the exact same result I would get if I were to use an apple TV and use airplay (but I don't have one to test).
So, to sum up my findings thus far: when using a Digital AV cable with an iPad (note, i think it needs to be an ipad 2 or newer), you ARE able to watch tv/dvr via the Dish Anywhere app. Viewing quality and resolution is effected. Watching the iPad Hopper transfer app, however is not supported with this cable.