Is a child at a US military academy considered a "full time Student?"

No.  They are cadets at a military academy, not full time students.

@aharden14 

Directions from the academies...for parents, indicate that in rare cases they might be able to claim the cadet is their dependent in their plebe year, but not in any subsequent years.

Select and Read the "Tax Tips for Parents" on the West Point Parents page  (even if your child is at one of the other academies...not sure where to find their guides)

Information for Parents | United States Military Academy West Point (usma.edu)