They will continue to promote programming uninterrupted, unless a tropical system is nearing.
That's another thing. A few years ago, a minimal TS (I forget which one) was moving parallel to the east coast. A few of the outer bands were reaching land, but the eyewall never even came close. TWC went wall-to-wall with it, and I didn't see a LF for at least 4 hours. And yes, there was severe weather in my area that day.
For me, my best bet is WGN's 24/7 news sister station CLTV. They normally do "Weather on the 1s." In times of severe weather, they usually have a small radar image running constantly in the lower left hand corner of the screen, even when they're airing their long form programming.