Will someone with a dampened immune system more likely develop encephalitis?

Yes: Encephalitis, inflammation of the brain, can be caused by viruses, bacteria, fungi, parasites, unknown causes, etc... Herpes types 1 & 2, epstein barr virus, varicella (chicken pox, shingles) virus, polio virus, coxsackie (hand-foot-mouth) virus, or mosquito-borne viruses can sometimes cause encephalitis. A weakened immune system makes one more likely to get these diseases and get encephalitis.

How dampened: Encephalitis is pretty rare, even in an immunodeficient person. Depending on the cause of the immune defect, someone may be prone to certain types of infections.