This is the reply to the email I cheekily fired off to the William H Miner Agricultural Research Institute:
Your question was forwarded to me. Whether or not cows will die if they're not milked depends on two factors: How much they're milking at the time, and how fast milking ceases. If a cow is only producing 20 pounds per day or less per day, she can be "dried off" (caused to cease milk production) simply by stopping milking her. That happens to almost every cow every year, and is a normal part of the "have a calf--produce a lot of milk per day---milk less and less per day--dry off--have a calf" cycle that's a cow's life. Done right, there's no problem at all.
However, if a cow is producing much more than 20 pounds per day, stopping milking her in one fell swoop will cause severe udder stress including inflammation, and the more she's milking the greater the chance that this stress and the resulting infection could kill her. Unfortunately, we have first-hand experience about this in this region (45 miles south of Montreal) since a few years ago we had a devastating ice storm that killed electric power for several days. One farmer who couldn't get a generator lost a bunch of high producing cows when he wasn't able to milk them. (He had about 150 cows, and milking by hand was out of the question.)
So a short answer is yes--under some conditions.
Everett D. Thomas
William H. Miner Agricultural Research Institute
P.O. Box 90
Chazy, NY 12921-0090
Phone 518-846-8020 Ext. 115. FAX 518-846-8445