Don't see why it won't work, provided you have a sling enabled hopper at home and don't mind downloading movies, then hooking up an HDMI cable (though I've never done that) from your tablet to your TV. I have streamed from my sling enabled hopper to a TV in my motor home via an iPad and 4G wireless hotspot.
The Chromecast question has me stumped. I have one, but only use it for streaming on a not-so-smart TV via wireless.
2003 Winnebago Adventurer 35U, 8.1 W-22, TruCenter
Fly R/C Helicopters