No, stress can't cause droopy eyelids.
Droopy eyelids or ptosis is caused by the malfunction, abnormalities or trauma of levator muscle and nerve, inflammation or lesions of the eyelids. People can't control their eyelid, because the muscle is not strong enough to do so.
Depression is an emotional discomfort which is likely to affect endocrine system but not the nerves or muscles.
Yes, it is possible for you to get droopy eyes because of depression. When you are in bad mood, your eyes will be easily dry because of the unwell blood circulation. The eyes surrounding skin will be loose which will easily be droopy. In order to prevent it, you could use the oil essentials to adopt on the eyes surrounding parts to moisture it. It is effective and workable which you could have a try.
Well, depression is really bad mood that can do harmful to our body. We always feel unwell, headaches and pain in chest. However, all these just we slow down immune system. Droopy eyes cannot be caused by depression. It is usually caused by allergies and some other eye problems.