But the whole idea of the alert is to let you know when bad weather is in the area. I'd rather get awaken in the middle of the night and then listen to the radio for details than get caught with my pants down ... well, asleep.
Keep in mind that during this scenario, besides several other adults being involved, it is not uncommon for 15-25 young lives are at stake. I don't mess around with real bad weather (interpreted as severe thunderstorms or tornados) when sleeping in tents.