Is it permissible for balding men to wear a hair system which consists of natural hair and is stuck on the head with adhesive glue?

The hair system also impedes water touching the scalp and can be refitted every 2 to 3 weeks as it is difficult to remove it everyday. Can one do wudu and ghusul with the hair system on?

If the hair system and adhesive constitute a barrier to the water reaching the skin then they must be removed before performing wudhu and ghusl