Yes, it can. A standalone mail server is one which does not use an ISP. Instead, it expects mail to be sent directly to it (using the SMTP protocol) and it sends messages directly to intended recipients by discovering the appropriate SMTP server to connect to for each recipient.
In order to use Softalk Mail Server as a standalone server you must have a permanent connection to the Internet with a static IP address. Also, you must arrange for your domain provider to modify the MX record for your domain to point directly to the IP address of the computer which runs Softalk Mail Server. Finally, you just need to install Softalk Mail Server in its Enterprise configuration by selecting the Standalone option when setup is first run. For more information, refer to the Softalk Mail Server help documentation.