As a person who drinks tea for 30+ year old in a country which is top 3 in world tea consumption, I can say that theanine works. The biggest advantage of it when compared to caffeine, it doesn't create that tension in the body. You just work and concentrate. While it's not as powerful as caffeine, it allows one to work very efficiently and for long hours, if they choose to do so.
Also, against the popular myth, black tea / theanine doesn't affect iron absorption that much (if any), if it was, the whole country would be anemic, and we are not.