Yes, they show as paused, and I can see the http address of the radio cast. I click the arrow to start it up again and it won't, it just goes back to a paused state. I have to unlock and bring up Safari (if I have left it at the home Screen) or if I left Safari in focus I have to refresh the page. The way it's acting I think it's a Safari issue with Bluetooth connections, or maybe this particular cast. I would expect that is a buggier scenario than the music app with Bluetooth.
That sucks. I've been frustrated by that before, just from random audio streams I've listened to from Safari. But I don't listen to audio through Safari too often.