Assuming they keep it streaming for us to watch, at what distance will it no longer broadcast?
Not very far. The batteries were reported to only last for 12 hours, and they are coasting for the first 6 hours, before it does the final boost to adjust to the final orbit.
How far can it get in 6 hours? Not very far. 11 km/s was the ultimate top speed we heard so less than 250,000km.