Are the dependents of deployed sponsors eligible to fly Space-A unaccompanied?

Yes. The DOD has recently updated the policy for dependent Space-A travel of deployed sponsors.  if the sponsor is deployed for any period of 30 days or more, dependents are authorized Space-A travel to/from CONUS and OCONUS locations, and within/between OCONUS theaters ONLY during the sponsor’s deployment. This authorization begins on the sponsor’s departure date and ends on the sponsor’s return date. Submission of a Dependent Verification Letter is required. For more details, please see Page 34, para. 4.9.b of the document linked below.

http://www.dtic.mil/whs/directives/corres/pdf/451513p.pdf