I've been considering doing something similar. My chromecast is currently connected to a Yamaha RX-V673 which outputs to a projector which I don't want to turn on just to listen to music. With my setup, were is what I found:
1) With the receiver set to HDMI pass-through, the projector must be turned on for the chromecast to work.
2) With the receiver set to HDMI up-conversion, chromecast works fine either way.
From this, I gather that when the receiver is on pass-through, chromecast is not getting something it needs, possibly a HDCP handshake, from a display device and won't work. When the receiver is on up-conversion, chromecast handshakes with the receiver and the receiver handshakes with the projector, and chromecast does not know or care if the projector is on or not.
So, to do what you want to do, chromecast is going to need something to which it can talk. I considered setting up a boombox, of sorts, in my bathroom with a small LCD display to make it all work.