Simple answer: Yes. It's like sitting next to a sick person on a bus; you'll probably get sick too. Necrosis can be caused by a number things but in many cases it is "contagious" in that it can trigger other colonies.
Longer answer: Typically when one coral is going there is a stressor in the tank that is affecting the others as well, so their already in a precarious state. Depending on what causes the recession, it can spread. In some cases the necrosis/recession is caused by protists (which can spread); protists are often present when LPS, such as flower pots, recede (aka "Brown Jelly"). In some cases the chemicals released by a dying coral are toxic enough to cause necrosis in a neighbour, who then starts to recede, who then... you get the picture. But it really depends on what caused the first one. Like KPG said as well, your corals were probably in a weakened state to begin with. My guess it that chemicals released by the dying coral just tipped them over the edge.
Typically if I see something receding quickly, I just cut my losses and get it out lest it should take down a few others with it. If it's a slower recession (over day/weeks) I tend to worry less and try to give it a chance to bounce back.
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