Yes, the Chromecast will probably continue playing a stream as long as nothing tells it to stop. However per Google's design guidelines, apps are not supposed to do this. They are suppose to shutdown the casting when they close. This may also depend on how the app running on the Chromecast is written. It is quite possible for a Chromecast app to automatically close itself if it doesn't receive some control message periodically.This is an interesting conversation
Here's my experience - If I initiate a stream using Deezer, I can close not only the browser but the whole PC, and my Chromecast continues to play and display albumart. I've enjoyed using an App named Dashboard Cast on my Android Phone, and it too continues to play on my Chromecast even if I leave my country and fly to Bangkok (which I did). Upon my return - when I turned the TV back on, the Chromecast was still playing.
So does also a number of Apps in the NatureCast series (Candlecast, FireplaceCast, RomaticCast, etc). They all seem to play forever. This leads me to believe that once a connection stream has been set up between the Chormecast and a server somewhere on the internet, it will continue to play forever until actively shut off (unless a timeout is programmed somewhere).
Do you agree?
Also since Android allows apps to run in the background without any UI indication some casting apps may seem like they have closed, but they may actually be still running in the background.
You could probably get the Chromecast to continue streaming from the LMS if you go to the Windows Task Manager and forcefully end the Chrome task while it's casting the tab.