While the electrodes do become charged, the amount of charge is not a fixed amount like -0.5 C. The electrodes become charged until the electrical potential difference between the electrode and the electrolyte is greater than the electrochemical potential of the reaction at the electrode surface. So the amount of charge depends not only on the battery, but also on the circuit.
For example, if it is in a circuit where the negative terminal is grounded, then the negative terminal will be uncharged and the positive terminal will be positively charged. Or if it is in a circuit where the positive terminal is grounded then the positive terminal will be uncharged and the negative terminal will be negatively charged. It is also possible to set it so that both terminals are positively charged (with the positive terminal being more charged), and it is possible to have both terminals unchargednegatively charged (with the negative terminal being more negatively charged).