Is this any business of the elders since the person was not IN anyway.
Legally, morally and ethically? No, of course it isn't. How you live your life whilst out of the organization is none of their business. Now, having said that, will those elders feel that way? No of course not. They will want to investigate any behaviors that they feel are inappropriate. If you were smoking while being in a disfellowshipped state, then they will hold that against you. They will make it that much more difficult on you in order to become reinstated. The standard wait time (subject to the elders' whim of course) is one year. However if you have been smoking or any other JW no-no, then the wait might easily be longer. Is that fair? No. Is that the way it is? Yep. Just remember when you apply for reinstatement you are playing by their rules.
If they aren't aware, is the person obligated to tell them
Nope. You don't have to say a word. However, there is one big caveat. IF they ever find out what you did whilst being DF'd, you will be disfellowhsipped again. IF they find out while you are still DF'd, it will add more time on to your reinstatment process. Realize you are dealing with massive egos. These men are kings over their little domain and they will mete out whatever punishment as they see fit.
I don't mean to sound harsh, but that is the reality. You could luck out and find a good, decent and kind-hearted elder, but they are in short supply. And even then if such one finds out that you did not confess everything, he will no longer be on your side.
You've got a tough road ahead NG. The deck is stacked against you and they will most likely make this experience as difficult as they can.