Actually, CA does. In CA they are called personal handgun importers. Military members can obtain handguns that are not on the CA DOJ approved handgun list in the state of their duty station and then if they choose to return to CA, they can bring those handguns with them and fill out the DOJ form to register the handgun in CA.
Anyway, to the OP.... your state of residence for the purposes of firearms transactions is the state you have permanent orders to (which appears to be TN). While you are stationed in TN, you can buy anything you want to in TN by using your active duty ID card and copy of your orders as identification/proof of residency to the FFL dealer.
See page 135-136 of the 2005 Federal Firearms Regulations Reference Guide (ATF Rule 2001-5):
http://www.atf.gov/publications/download/p/atf-p-5300-4.pdf
You are not subject to MA firearms purchasing laws at this time, because for the purposes of firearms transactions, you are NOT a resident of MA, unless you are present in MA with the intent of making a home there - which you are neither, at this time.
When you return to MA at any time, for any reason, you immediately fall under the MA laws for possession of firearms. That means that you must have the appropriate MA license to possess whatever guns you intend to bring with you into MA. The licenses will have to be obtained in advance of you bringing those guns into MA.
If it were me, I just wouldn't go back to MA and stay in free America!