I'm not sure about your theory. Instant geyser has a heat exchanger and copper pipes wrapped around it, so virtually all of the heat is absorbed by the water in copper pipes. That's why these are considered efficient heaters and also why after its been running for a while, you can easily touch the body of geyser - at least I can on mine.
Secondly, the weather box is open from the bottom to let fresh air in, and the flue/cowl/cap on top is designed to prevent wind blowing into the geyser and blowing out the flame. Apparently, these are quite common in South Africa - as that's the only country where I see people selling these weather boxes.
As an experiment, I will get one made and report back the result as next few months will be windy in Lahore.