plenty of songs are mistaken for traditional,Fiddlers Green,Bring us a barrell,are two that spring to mind,.
whether they are entering the revived tradition,or whatever you want to call it,the important thing is they are being sung and passed on orally.,often without the singers knowing they were composed.
The only person I have heard of who stopped singing a song when he discoverd it was not traditional but composed,was BobDylan.