No, guests who do not have a balance due will not receive a balance due reminder email. However, you must set the condition for the email to send in correlation with a balance due date.
For example, set the condition to send when “Balance Due” or “x Days Before the Balance Due Date at xx:xx am/pm.” If you set it to send “30 Days Before Arrival” they WILL receive the email, because it is not associated with the balance due date.