It depends on the type of water and the person. The more pure water is the faster it will generally enter the body. That is provided it is drunk on an empty stomach since minerals and foods can affect absorption. Of course you will also pee it out faster. This is another reason I prefer spring (mineralized) water, which is absorbed at a much more even rate. And a healthy person can drink more water than say someone with kidney failure. And in warmer climates you will need more water than in a colder climate due to losses through sweat. There are other factors such as the consumption of alcohol, the use of diuretics like caffeine, etc.
And yes, a person can drink too much water. Water intoxication adversely affects the electrolytes leading to brain swelling, which can kill you.