A general rule is that in order for wudu or ghusl to be considered valid, it is necessary for water to make contact with the skin. Failure to do so, will deem the wudu or ghusl invalid.
In this particular scenario, if the waterproof makeup prevents water from making contact with the skin, as implied by the term ‘permanent’, then any wudu or ghusl performed over it will be deemed invalid. Consequently, prayers performed with an invalid wudu or ghusl will also not be considered correct.