https://www.dol.gov/agencies/whd/fact-sheets/28o-mental-health

yes, it counts. but you still need a doctor to sign off. you might have a hard time if you haven't had an inpatient stay or something serious like that going on. you can't just be like "I'm depressed and i don't feel like going to work for two weeks" and get FMLA. but if you feel like you really need it, get the paperwork and talk to your doc.