With the receivers popping up at Walmart and the corner drug store, I would think awareness must be getting fairly high.
I've also seen a fair # of people not understand what to do when the hazardous/tornado sirens go off, but there's some towns that have done enough public education that they use the same sirens for warnings when there's a HAZMAT concern at the towns manufacturing plant.
The point of this is some people will be better of hearing a siren, some will be better listening to a radio, some will do better with the weatherman on TV telling them what to do, some of us flip over to the local weather spotting HAM channels ...Officials need to be able to quickly activate all the means available to them to warn people, and it's up to the general public to have something in place that they know how to understand to act accordingly.
And yes there are dedicated weather radios, and there's even weather AM/FM alarm clocks (however they all look goofy and nothing my GF will let sit on her nightstand
) that you can set to only tune in when there's an alert. And alot of companies are doing a good job of building them into other radio type things to encourage people to get the alerts.