The key thing about adding water into an ICE being fed with hydrogen or oxyhydrogen is the cooling effect and so its predisposition to inhibit pre-ignition. It will also of course slow the burn rate down.
I've always considered drying the oxyhydrogen going into an ICE to be positively detrimental, but there are those that go to the extra time and trouble to do just this. To my mind the tiny amount of liquid water that would reach the combustion chambers when fed into the air stream is negligible, and would have to be in order not to quench the flame altogether.
It is a fine balancing act to get it right, and yes to gain maximum benefit you would need to slightly adjust the engine timing, but it is worth it.
I found that our old Land Rover always ran much more smoothly and seemingly with greater power available on cold misty mornings due to the great amount of moisture in the air. And indeed I do now employ a water injection set up similar to that described in the second link of my first post.
I first discussed this with William Rhodes quite a few years back, and in fact it was he that lead me to follow it up, as he had toyed with a set up whereby air going into the engine was drawn through a maze of wet baby nappies. Though the bigger American vehicles had much more room in the engine bay for such a set up, which was not so practical for European vehicles.