Maybe. It depends. And a waiver is possible. Look at the standard,
http://www.dtic.mil/whs/directives/corres/pdf/613003p.pdf, around page 47. It states as disqualifying:
f. History of depressive disorders, including but not limited to major depression (296), dysthymic disorder (300.4), and cyclothymic disorder requiring outpatient care for longer than 12 months by a physician or other mental health professional (to include V65.40), or any inpatient treatment in a hospital or residential facility.
g. Depressive disorder not otherwise specified (311), or unspecified mood disorder (296.90), UNLESS:
(1) Outpatient care was not required for longer than 24 months (cumulative) by a physician or other mental health professional (to include V65.40).
(2) The applicant has been stable without treatment for the past 36 continuous months.
(3) The applicant did not require any inpatient treatment in a hospital or residential facility.