> Diphenhydramine as a first generation antihistamine acts on a large number of receptors and can even be used as a mild anxiolytic, so I'd guess it could very well have antidepressant effect.

It does, and this observation led to the development of dedicated antidepressant drugs. There are several such cases where interesting side effects turned out to open a world of possibilities, including an anti-TB drug that also led to antidepressants, and of course Viagra.