Is it possible for sunglasses to cause depression, due to lack of sunlight to the eyes?

No. The sunlight/depression link has little to do with your eyes. Your skin absorbs the light, and in some cases prevents depression. I think even blind people benefit from sunlight in this regard.
No. If you are referring to seasonal affective disorder (sad), there may be a link with sunlight and mood. Sunglasses, however, do not occlude 100% of sunlight from the eyes so they should not affect it. There is also some thought that sunlight on the skin is enough to help reduce the symptoms of sad. There is no association between general depression and sunlight, however.