That "Yes or No" just made me think that you might only want the answer.
Both Sauron and the balrogs were maiar, balrogs being spirits of fire (like Arien). There were never that many balrogs, but they had their own, certain characteristics (whips of flame and whatever). Tolkien spoke about balrogs and he spoke about Sauron, but he never even hinted that Sauron might have been a balrog. Usually I don't think that because Tolkien didn't say something it didn't exist, but if Sauron had been a balrog, Tolkien
would have said it. It's a thing that has much more to do with the mythology than eg. the characters using bathroom.