My thoughtful contribution to this thread:
Gothmog was Lord of the Balrogs, so if Sauron was a balrog, he would had been subordinate to Gothmog. However, we know that Sauron was NOT subordinate to Gothmog and was Morgoth's lieutenant. Therefore, he could not have been a balrog.
When I saw the thread title, my knee-jerk reaction was just to say "***???" and leave it at that. However, I resisted the temptation to be an irresponsible and flippant thread-basher. Someone had better appreciate the extra effort...