My ex got right into the whole supplement thing - to the point he was mixing these powders like some mad scientist (he is pretty smart) and he never came up with any sure-fire answer to anxiety/depression. He also used to grow all sorts of ethnobotanicals.
I think they can help but will never be as effective as pharmaceuticals like benzos. I take some myself but yeah at the end of the day if my anxiety is bad I'd much rather a Mogadon (medium-acting benzo) or some oxycodone.
Alcohol actually trumps EVERYTHING in terms of its (immediate) anti-depressant effect but its depressive effect, when it wears off, also trumps everything.
P.S. I'm not trying to rain on anyone's parade or wanting to start arguments I think it's great if something like L-Theanine helps. I'm just saying I've seen someone take the supplement thing to the extreme and he never found the perfect remedy for anxiety/depression.