To receive incoming messages to an email address, you can enable email forwarding in your Texty Pro account. This will notify you of new messages even while not signed into your account. To set it up you must log into your Texty Pro account and update your settings.
You can enable it, disable it, and change the email address as needed. You will receive an email with the contents of the incoming message, but you must log into your Texty account to respond.