The gemara in Gittin 42b discusses whether a slave owned by a Cohen that has been freed, but has not been given a formal document of freedom (גט שחרור) can still eat Terumah. The gemara attempts to bring a proof that he may eat Terumah from the following *Mishna* (Yevamos 99a): 
>כהנת שנתערב ולדה בולד שפחתה הרי אלו אוכלין בתרומה וחולקין חלק אחד על הגורן הגדילו התערובות משחררין זה את זה

>If the wife of a Cohen mixes up her child with her maidservants' child, the 2 children may eat Terumah, and collect a portion of Terumah (together). When they grow up they both free each other.

The implication is that the slave is effectively considered "freed" since you cannot work them since they may be Jewish, yet they were not formally freed with a גט שחרור and the *Mishna* says that they may eat Terumah.

The gemara rejects this proof:
>הכי השתא התם אם יבא אליהו ויאמר בחד מינייהו דעבד הוא קנין כספו קרינא ביה

>That case is different because If Eliyahu Hanavi would come and identify which one is a slave, they would indeed revert back to being in the possession of their owner.

From here It seems clear that even a child who was raised as Jewish, but Eliyahu Hanavi revealed that they are not, they would indeed have the status of a non-Jew.