Well, it depends on the type of alarms sounded. There have been quite a few good studies on the psychology of panic released in the last few years, in which the human response to disaster has been analysed. To reduce the findings down to a simplistic level, an alarm coupled with the presense of authority figures giving direction and clear cut instructions on what to do, results in more lives saved than when people are left to their own devices. Hardly sounds like a rocket-science discovery, but a surprising number of people who should know better, many in positions of authority who may need at some point to actually to supervise a fast evacuation, still subscribe to the 'people are like ungovernable cattle in these situations' theory. Panic tends to result when people, usually at the back of the line, begin to realise that not everyone is going to escape. Take, for instance, the Beverly Hills Supper Club Fire, which highlights both points I am making. In that case, a fire broke out at the front of a large nightclub establishment, at the rear of which was a dinner theatre where 1100-1300 people were awaiting a performance by John Davidson. The people in areas of the building from where the fire was visible (perhaps as many as 2000 people) evacuated successfully, but the people in the theatre were unaware that a fast moving fire was bearing down on them. An 18 year old busboy, who was aware of the fire destroying the front end of the building, took it upon himself to go onstage (the owners of the nightclub, although presnt and aware of the fire, did not) to advise the audience of the fire and the location of the (obstructed) exits, in a clear and direct manner. The result was that the majority of people in the room escaped, despite the obstructed and inadequate exits, by taking immediate action. They had A) coherent instructions, from B) a staff member who C) remained calm. The 166 people who died in the showroom (2 two women were trapped in a dressing room in another part of the building; the only non showroom fatalities) were those who panicked at the last minute, as the room "flashed over," and jammed towards the exits, in one case piling up nearly eight feet high as they attempted to gain 'advantage' over those ahead of them. Had it not been for the busboy, given the conditions in the room and the speed with which it burned, fatalities would likely have approached 90%. Had those in the room been given just another three minutes (that is to say, if someone had sounded the alarm slightly earlier) the situation which caused the deaths would likely have been avoided.
It is tempting to play 'second guess' with the Titanic evacuation, but the fact is that for every argument against the means by which the ship was evacuated there is a compelling counter argument, so the best one can hope for is a 'draw.'