After reading the above, I did a quick check. I have an original Hopper with a Sling Adapter and an OTA adapter. I have a single television, no Joeys.
I got no message on the screen that remote viewing was taking place. The Hopper viewing was uninterrupted.
I was able to stream local OTA, but the channels were off. When I tuned to 03-1, I got 03-3 instead.
When I pressed the Red button, it shows what each tuner was tuned to, and one of them had the Sling icon. I suspect the message Jim got about remote viewing in use was because his Hopper was already recording 2 channels, and thus the Sling took priority over the local connection for the only available tuner.
Picture quality is pretty good on a small screen. It's hard for me to compare a 7" tablet to my 50" plasma, though. I would guess that a picture quality snob would not be happy with the streaming picture.
With local streaming, I was getting an HQ stream of 1300Kbps. There was no difference in streaming data usage in Standard Quality. Divide that by 10 for approximate KB/s and you get 130KB/second. Rough math says about 8MB/minute. I know of no Dish-imposed limits on Sling viewing, either in time or programs. My efforts to stream over 3G have been very choppy at best, and HQ was not possible.