I think you are asking a legal question and really need to talk with a lawyer. Preferably one that deals in real estate.
I think you potentially open yourself up to the LLC being broken if challenged by not having the debt in the name of the LLC. But I don't know that for sure. I say spend the few dollars to talk to the attorney get the right answer, write of the legal fees off in the LLC and move on with your life.
As an accountant, if there is any chance you are going to sell the property in the next 3 years, I wouldn't put it in an LLC though. As you will lose the exemption on the gain if you do ($250k single $500k married). Curt can probably confirm/ or correct me if I am wrong.