Yes. Any e-mail you have stored on the server counts as storage for your account. This is one reason we recommend not storing e-mail on the server. Once you download and read your mail, you should ensure that your e-mail client deletes the mail from the server.
In the configuration settings for your e-mail client, make sure that you do not have the option selected to "Leave mail on server" if you do not wish to store e-mail on the server.