No, not usually. Some women will experience HG straight through the pregnancy and even through labor, delivery and for a (very) short time after the delivery but that’s just not the norm when it comes to HG.
I had hyperemesis gravidarum two times, and both times I stopped throwing up around 17 weeks with nausea greatly improving by the third trimester. The timeline for hyperemesis that I noticed in my own pregnancies was:
6 weeks: Onset of severe morning sickness (I usually didn’t feel many symptoms when I first would find out that I was pregnant)
8-12 weeks: These were the absolute worst weeks for me with constant sickness, nausea and dramatic weight loss.
13-16 weeks: Vomiting began to lessen, and I would go whole days without getting sick at all and was able to manage my symptoms with medications. Usually, I would go in a pattern of like one good day then two bad days through this period.
16-28 weeks: Still experiencing some nausea that could be controlled through proper diet, exercise and getting enough rest (with several breaks throughout the day). Almost no vomiting except random bouts.
28 weeks - delivery: Only experienced random bouts of nausea but did deal with a lot of acid reflux!
Every woman, every pregnancy, and even every HG pregnancy is different but take solace in that it almost always gets better (and once that baby is out you’ll be cured!)