A short answer, No. I googled oxygen deprivation depression and came up with nothing. If this were true there would be reports of it available and we would all be dragging oxygen tanks behind us. I have noticed several threads here and on other communities about these types of unfounded cures for depression and bipolar. Again, no proof of this hypothesis exists.
stress can feed depression and stress chemicals are cleared out of the brain by oxygen. I am interested in this too.
I have never hear of any studies that would indicate such a thing. Depression is often caused by chemical changes deep in the brain and adding more oxygen would do nothing to ease the suffering depression causes.