Can eclampsia cause brain damage?

Eclampsia. This is unusual, but can happen. Eclampsia is preeclampsia with seizures. It is unusual for these seizures to cause brain damage, but not impossible. Early treatment will usually eliminate that problem.
Yes. Eclampsia is characterized by hypertension which may be difficult to control and seizures. Patients who become eclamptic may have a stroke or intracranial hemorrhage, which will cause brain damage.