Thanks, Erik.
I had also submitted a support request asking for this, and was given a good suggestion in the interim.
I figured I would post it here in case anyone was interested:
"It is possible to have state changes done automatically through the dispatch options, possibly combined with closing rules to have them set to the closed state, for situations where you only need a ticket for tracking purposes. This would require you to send an e-mail to the help desk instead of creating it through the help desk however. The dispatch options and closing rules can be found in the 'Configuration\E-mail Settings'."
Thanks.