Celiacs don't have a weakened immune system just because they are suffering from Celiac disease.
However the person with Celiac disease may already have a weakened immune system but the Celiac disease itself doesn't weaken a persons immune system.
Actually when someone does have Celiac disease they usually have a stronger immune system than those people who are not Celiacs.
Celiac disease itself will not kill you but if you continue to eat foods that contain gluten when you do have Celiac disease then it can damage your intestines which can then lead to death.
Celiac disease is just an immune disease which means the person with Celiac disease can't eat gluten because it will damage their small intestine.
As long as you stop eating gluten the Celiac disease should cause no other health issues.
Celiac disease is not a deadly disease that progresses like other diseases such as cancer so you're usually safe when you do have Celiac disease.
However when Celiac disease is left untreated the Celiac disease can sometimes lead to the development of other autoimmune disorders like Type I diabetes and multiple sclerosis, and many other conditions, including dermatitis herpetiformis (an itchy skin rash), anemia, osteoporosis, infertility and miscarriage, neurological conditions like epilepsy and migraines.