Is it possible to modify the modify the email that Appian sends when a new user

It is. You can control templates that are used for create user/reset password emails with these properties: conf.security.pw.CREATE_USER_PASSWORD_JSP and conf.security.pw.RESET_PASSWORD_JSP.
You can copy existing templates to createUserPassword_emailHtml_custom.jsp and resetPassword_emailHtml_custom.jsp and update them. You will also need to have corresponding internationalisation resource bundles.
Obviously this is a customisation so you will have to do this every time you upgrade Appian and there is no guarantee that it will be supported in future versions. Appian has already deprecated conf.security.pw.RESET_PASSWORD_JSP and conf.security.pw.CREATE_USER_PASSWORD_JSP properties but it is not clear when they will be removed.

Another option is to create a custom process to create a user using the Create User with i18n smart service and integrate the custom e-mail in there.