Yes, drinking water will help reduce red eyes which are caused by the eyes infection and so on. You could also use the eye drops to release the symptom of red eyes. You should have the good rest for the eyes, not sitting in front of the computers for a long time. You could not smoke or drink which may stimulate your eye nerves.
Usually, red eyes often company with dry and itchy eyes. If so, Drinking more water may help the red and itchy eyes to some extend. but if you get red eyes because of seeing too much computer, tried and stay up to in middle night and get injuries as well as infection, allergies etc, drinking more water do nothing to your red eyes. So, if you noticed red eyes, you'd better have your eyes checked by doctor so as to know what causes it, thus you can treat your eyes in the right way.
Red eyes occur when people are tired, or lack of water, etc. So, you can see that water can help people get rid of red eyes. However, the basic reason for red eyes is tiredness, so relaxing more is always important.
Take a break every hour. Massage your eyes whenever your eyes get tired. Make sure you have 8 glasses of water every day. You can use artificial tears to help you get rid of red eyes faster.
All right, from what I see, you have got some troubles and are eager to get rid of those red eyes. Anyway, it is true that drinking water does good to your eye health. But since red eyes are mainly resulted from some bad use of your eyes, thus, it would be wise for you to figure out where went wrong, and just get proper use of your eyes. Sometimes you would be much better if you take some breaks and get eye drops.