This is definately a possible symptom of pregnancy. I am almost ten weeks myself and am not only sick in the morning...i'm sick all day. I haven't been able to eat much at all. My doctor told me that if it got to a point where i couldn't eat anything that there are nutritional supplements you can use to make sure your properly nourished for the baby as well as yourself.
Yes this definatly happens to some people during pregnancy, it happend to me this time although my sickness has gone now and im 13wk 3 days, but yes every woman and pregnancy is different, some women are sick ALOT more than 3 times a day so dont worry. Just made sure you drink plenty of fluids to keep hydrated!!.. =]
For some women this is definitely possible. The important issue is to stay hydrated. And you should also notify your doctor so that they can help you overcome this and stay nourished.