Judge Bates says yes, at least for detainees not from Afghanistan who have been detained at Bagram for several years:

Under Boumediene, Bagram detainees who are not Afghan citizens, who were not captured in Afghanistan, and who have been held for an unreasonable amount of time -- here, over six years -- without adequate process may invoke the protections of the Suspension Clause, and hence the privilege of habeas corpus, based on an application of the Boumediene factors. Three petitioners are in that category. Because there is no adequate substitute for the writ of habeas corpus for Bagram detainees, those petitioners are entitled to seek habeas review in this Court. Accordingly, respondents' motions to dismiss the habeas petitions of petitioners al Maqaleh, al Bakri, and al-Najar are denied. As to the fourth petitioner, Wazir, the Court concludes that the possibility of friction with Afghanistan, his country of citizenship, precludes his invocation of the Suspension Clause under the Boumediene balance of factors.

  Judge Bates's opinion strikes me as a careful and thorough application of Boumediene. The result is plausible under that case, especially given the vagueness of Boumediene and its multi-factor approach.

  At the same time, my guess is that the Supreme Court would (will?) look at this differently. Judge Bates ends up focusing a lot on the practical control that the U.S. exerts at Bagram, especially around page 30:

Perhaps the difference in jurisdiction precludes the United States from operating at Bagram, as it does at Guantanamo, entirely free from the scrutiny of the host country. As a practical matter, however, when assessing day-to-day activities at Bagram, the lack of complete "jurisdiction" does not appreciably undermine the conclusion that the United States exercises a very high "objective degree of control."

  My guess is that the Supreme Court would weigh freedom from scrutiny by the host country as a formal legal matter as more important than does Judge Bates, and that the Court would end up effectively limiting Boumediene to Guantanamo so that it generally does not cover detention elsewhere. That's my guess, at least. Obviously this will be an important case to watch.