A:
All Chromecast does is allow you to CAST whatever device you're viewing on your phone/tablet/pc 's APP (Hulu, Netflix, Espn, etc) on to be shown on the TV. If the APP itself doesn't work with Chromecast, it won't work for you.
For Example, Sling Box recently updated their APP to allow Chromecasting, so we were watching our home TV recently in Florida via my cell phone casting the Sling Box app on it on the TV, which our cable box has all the cable channels, dvr, etc etc..
I'm pretty sure HBO Go app is Chromecast-able, so if HBO is where you're wanting to watch your On-Demand Movies, you should be good.