Maybe I'm missing something, but I've been using the app via Bluetooth for over a year. Not to play the rendered audio, but playing the tracks works perfectly, enough so that it was six months before it occurred to me to pre-render the tracks, as I play most of my tracks from iTunes via the Big Button app.

I have had occasional dropouts with the Belkin device, but quite infrequent, and mostly due to momentary power interruption (the Belkin power supply cable is cheap and inflexible, so stage vibration can be enough to cause a dropout, just set it on something soft if it's an issue.)