If a person has bilary atreasia will they possibly need a liver transplant?

Perhaps. Biliary atrecia, non formation of extra hepatic bile ducts, in type I &ii common&c hepatic duct are intact, type iii right and left hepatic ducts are involved, most of the time kasai's procedure is enough (portoenterostomy) & not liver transplantat in a different condtion intrahepatic biliary hypoplasia, where intrahepatic biliary ducts are not formed, will need.
Yes. Liver transplantation is the definitive treatment for biliary atresia for selected patients, mostly in their childhood. Fortunately in experienced hands the results from liver transplantation are excellent and most children can go on to have relatively normal & healthy lives after their liver transplants.

Related Questions

When is a liver transplant necessary if I am suffering from biliary atresia?

See your doc. Can't tell when you are ready for a liver transplant. There are different gradations of severity of biliary atresia, and liver abnormalities due to it. Your picture looks like you're an adult, so it is different than infantile biliary atresia. Check with doc re: liver chemistries, liver damage, perhaps biopsy changes. See if you can get surgical treatment. If failed, may need transplant.
Eventually. When a patient has biliary atresia then progression of liver failure may be slowed permanently or partially. Liver function must be continually monitored. Any rise in liver function tests or signs of coagulopathy or portal hypertension need to be assessed by liver transplant specialists.