It is true that emesis does contain HCl or hydrochloric acid from the stomach. Periodic morning sickness or nausea and vomiting are fairly common in the pregnant female but these episodes are not harmful unless they become intractable. Intractable nausea and vomiting means that the nausea and vomiting episodes are continual and prolonged. In other words, the female has continual nausea and vomiting with repeated episodes.
With intractable nausea and vomiting, the danger comes from the loss of electrolytes in the emesis, not from the HCl coming into contact with the esophagus or mouth. Repeated episodes of vomiting or diarrhea cause us to lose fluids and electrolytes like Na., K., Cl., etc., this can become harmful in the pregnant or nonpregnant female.
This is a good question.
It is quite rare for a women to develop problems resulting from vomitting during morning sickness, but it isn't unheard of. Hormonal changes in a pregnant woman's body build up the necessary defenses to protect the mother from such long term damage caused by the changes she undergoes as the child grows inside her.
That said, though in the majority of cases it is not harmful, in rare extreme cases a woman can develop similar long term problems that those with acid reflux experience resulting from stomach acid in the esophogus and mouth. This would more than likley be seen in a woman with hyperemesis gravidarum (extreme morning sickness).
When a person vomits, they are expelling the contents of their stomach, which does include stomach acid. This is what causes the burning sensation in the throat and the acidic taste in the mouth when you get sick.
In order to cause problems like erosion of the esophageal lining, it needs to be a persistent problem for a long time, longer than morning sickness usually lasts. Sometimes people who suffer from bulimia will have problems from stomach acid, or those with long term acid reflux disease, but not from morning sickness in most cases.