Sure, I'm not saying that it's completely useless - it gets the warning out and that's often all that's required to save lives. Our broadcasters stay on the air for the duration, but they mostly just repeat the fact that there's a tornado, seek shelter. If you want to know if it's on the west side of town, or the east side of town, or if there's one forming south of you going north, then it's time to break out the scanner and listen to the spotter network. By the time the broadcasters get wind of what's happening you could be gone. 5 minutes is a long time.
I guess I'm talking about getting breaking updates as opposed to information that may be too old to matter much. Now, if you've already taken shelter when the sirens were first sounded then it really wouldn't matter too much. But I prefer to know more than "there's a tornado in the area, you could be affected." If you take your portable TV in the hole with you, you're still really only going to know that "there's a tornado in the area, you could be affected." And that's great if that's all you want. I want to know about which field the tornado is in, them funny looking clouds that just started rotating, that other tornado that is on the north side of town but going north, etc.
Then again I could just be paranoid about tornados after 1980 when half the city was leveled.

I think this would be especially true in a man made disaster such as chemical leaks and such. That seems like such a fluid situation that you would not want to wait for information updates. If you are evacuating, doubly so.

So feel free to take your portable TV because there's certainly no harm in doing so, but augment your assessment capability with a good quality portable scanner.