Being an authorized signer of a LLC and not an owner, will I be responsible if a deposited check is withdrawn and as a result balance is negative?

It depends what the account agreement says in part.  However, in general, if you deposit a check, your endorsement is a guarantee of that check.  If the check is large enough, and if the check was a fraud, you could have personal liability.  However, the bank would have a burden of proof.