The bank is considering offering the chance to win a prize to those who sign up for e-Statements. Would this be considered a lottery since it is not open to the public i.e. only those who have an existing account with us, and in order to receive a chance, the consideration aspect is them having to sign up for e-Statements?

To my understanding, under Georgia law this would be considered a lottery becuase in order to win the prize you would have to have a deposit account.

Can the Bank treat this as an exception and go forward anyway?
What would be the penalty?
Comments and opinions will be welcome on this topic.

Treat it as what kind of exception? What was asked isn't allowed, it's illegal.

Here is something you can refer to that may be helpful:

http://law.onecle.com/georgia/16/16-12-22.1.html

Thank you RR Joker for the additional reference on this topic.
Greatly appreciated.

Your welcome