No, Your felony charge will not drop unless there is some reason for it to be drop, IE, self-defense and you kill the person, you are charged with murder, and its dropped. As I stated unless there is some reason for it to be dropped lower it wont be. And a court appointed Attorney wont hurt you, in most cases its better because it wont put pressure on your family to pay your lawyer.

But since it is your first offense, depending on the crime itself, they could show you kindness and lessen the term you have to serve.