What is the reasoning behind NOT notifying them?
1. you'll be back to your permanent address anyways, and they already know where to find you.
2. there's a statute mandating notification of "ANY" change of address.
It just seems to me that there's not a whole lot to gain from not notifying, and plenty to lose.
As a practical matter, any correspondence from the DESPP regarding your permit status or firearms/LCM registration will need to reach you in a timely fashion as you may be required to timely respond. It's in your interest to ensure that the DESPP can get mail to you. Sometimes you are required to meet strict deadlines upon notification of any issues by DESPP...you definitely WANT to get their mail. Don't jack around with your license.
Some folks may take a different view...and they can take their chances. If you have a problem with sharing so much personal info, take it up with your elected representative.