In practice, it's a bit worse for digital. The decoders seem to lose sync easily and just go black for a bit where the analog would have given a couple frames of static and then a watchable image. If it happens frequently enough, you get a black screen and silence from digital where you would get a staticy but watchable picture on analog.
Multipath on a digital signal is a serious issue where on analog, you will actually stop noticing the ghosts after a few minutes.
On the old analog NTSC, the audio was on a subcarrier such that even if the video was an unwatchable mess, you might get decentish audio because of it's minimal demands on signal. Alas, in digital TV, it's all packets in the same stream and the decoder either can't or won't bother decodingh the audio if the video is lost. That's a real problem since is the video is disrupted, you can often follow a story OK, but when the dialog keeps going away you quickly get lost. Same problem if you're trying to get important weather information.
To top it off, as you say, they snuck the power down when the transition happened.