I don't think I'd want this to be automated, because it would be obnoxious. I might not agree with the game about what constitutes a disaster or how I want my dwarves to respond to it.
So I think we're looking for basically looking for two game mechanics here, which take some of the ideas we're seeing for the military in the next version and extend them to squads which are not activated into the military:
1. Ability to place civilian squads on-duty and in alert modes, so that your siege operators and lever-pullers will carry food and water, not desert their stations until released, and be far less sensitive to job interruptions by enemies. You'd handle small emergencies and routine sieges this way, by going to a squad you'd reserved for just such occasions and telling them it's time to go. It could be useful to prevent disasters by saying that one dwarf will be stationed by the emergency shutoff for the magma pumps at all times.
2. Better labor handling, so that instead of individually toggling a lot of labors for a lot of dwarves, I can take some squad and say "until I say otherwise, everyone in squad A has stone hauling enabled and nothing else, and everyone in squad B has health care enabled and nothing else" until the collapsed dining hall is taken care of. Squads could have labor settings like individual dwarves, and the on-duty status would determine whether dwarves used their own labor settings or those of their squad. This would be useful for organizing extra workers to handle larger disasters.
These sorts of things would have a lot of lovely uses besides handling emergencies. For instance, after a siege, activate a special corpse-hauling and trap-cleaning detail, and call up all the furnace operators on overtime to melt armor. Or during construction of a major project, take your pump-operating military trainees and press them into service as strong, agile masons & mechanics.
They would also provide useful occupations to migrants. Besides your military, your fort might also have a sizable paramilitary organization who keep the control rooms, siege engines, and hospitals manned, haul ammunition for crossbows and siege engines, and are available as labor for special projects.
I'm definitely in favor of being able to designate squads as firefighters and have them carry buckets at all times. They should probably use something similar to the way that soldiers presently select targets to pick fires to put out and wounded/unconscious dwarves to rescue. I order the squad into some area, and they start going that direction and dealing with problems as they find them. This should probably be a duty of the fortress guard most of the time, after the upcoming squad reform hopefully makes guards less irritatingly useless. Extra non-Guard firefighters could be drafted in small pre-guard forts or huge fires.
I'm correspondingly in favor of having more ways to set fires, and more ways to set your fort on fire. Furnaces and kitchens could be prone to accidents by unskilled operators, tantrumming or insane dwarves could commit arson (damn I'd love to see a dwarf fail a mood and proceed to set fires all over the fort), and sieges could do all kinds of fun things.
Oh, and if we have the ability to post dwarves constantly in control rooms, I think children and insane dwarves should love to pull unattended levers...