In the 15 years I worked in medicine, primarily at University of Maryland Hospital and John's Hopkins Hospital, I only saw 2 incidences of Boerhaave's syndrome, both of which were successfully treated with surgical intervention. One of the patients was relatively old, I'm guessing in his late 60s, and had suffered from severe acid reflux for two decades, which likely caused esophageal erosion. In his case, the esophageal lining was so thin it was nearly impossible to suture. The second case, which was a relatively young lady, seemed to have no underlying cause, and she spent many, many weeks in intensive care after surgery due to secondary infections that had set in shortly after the esophagus leaked into the thoracic cavity. She claimed that it occurred when she coughed and she felt a horrible pain in her chest and abdomen. Unfortunately, it was not immediately diagnosed in the ER, which led to further complications.
Usually, but not always, Boerhaave's syndrome requires a significant amount of internal, esophageal pressure to cause the esophagus to rupture. When I person is seasick, at least from my own personal experiences, it doesn't take long to completely empty the stomach contents overboard. I believe it would be a bit difficult to build up a significant amount of internal, esophageal pressure, even when experiencing dry heaves, when the stomach is nearly empty. But, I guess anything is possible, especially when it comes to seasickness.
I would hope that if someone developed seasickness to the point where they were in imminent danger of dying, they would take appropriate action--even if it meant taking up another form of recreation on dry land.