There are pros and cons to that.
Advantage is of course you get peace and quiet like that. No TV might feel more relaxing.
Downside is someone might plug the TV in again which will turn it back on to Fox. Changing the channel means you can show unbiased news and maybe if for example you change the station to PBS, people will get educated. People might leave it on the channel you changed it to due to apathy. A TV that's off is more noticeable.
I'd recommend if it's possible especially if you're the only one in the room at the time consider going into the channel editor and removing Fox News and other propaganda stations from the channel list.
That's really annoying. Do you think they'd notice you using your phone to change the station and possible remove Fox from the channel list? Is there windows in the building with the TVs? There are some high power IR blasters that might let you change it from outside.