That depends entirely on your mail server. My advice would be to simply set up another forwarder and test it out.
I know, for instance, on my server, I can set up aliases in cpanel like so:
support@mysite.com > |/usr/bin/php -q /home/kelli/public_html/osticket/api/pipe.php
support@mysite.com > kelli@mysite.com
I just set it up as a second alias and it works. Your mileage may vary.
If that doesn't work for you and you really need the messages to go to a real inbox, I would suggest you use email polling on a cron job instead and just set up helpdesk@ as an actual mailbox that your staff can check (though piping really is easier and more efficient if it will do what you need).
Oh, and unless you're doing this because you need the actual email messages themselves, another option would just be to set up a new ticket alert that sends an email to personal@ and lets the user know a new ticket has been created.
