I don't doubt the military personnel and commanders, on their own, would extend a welcome to Palin, but in all probability Obama would order them not to.
Several months back President Bush made plans to visit with the troops at Fort Hood in Texas as a morale booster relating to the Hasan murders. Obama told him no, and Bush, wrongly in my opinion, acquiesced without protest. The point is Obama would not allow military personnel to help Palin. And ironically, it would be one of the few things he's done which would be justifiable legally.
"Army officials would not comment, so we spoke to Bush spokesman David Sherzer, who was happy to set the record straight.
Sherzer described the visit as being "as spontaneous as a visit from a former president can be" — it was planned that same day. But Sherzer told us that Bush’s visit was coordinated with base officials, that he did not refuse escort, and that he did not overstay his welcome. As for the part about President Obama telling him to leave, Sherzer said that’s simply not true."
http://factcheck.org/2010/02/bush-at-ft-hood/