Will drinking a cup of coffee before I sit down to work improve my concentration, compared to drinking a cup of water?
Caffeine is a stimulant which makes you feel less tired and, for athletes, delays exhaustion. So if the alternative is being asleep, caffeine cetainly helps.
The other issue is that the regular use of caffeine leads, as with other psychoactive substances, to dependency (tolerance or addiction are other words used). In such cases, lack of caffeine leads to withdrawal symptoms such as drowsiness and irratability. For dependent individuals, a cup of coffee will remove these symptoms in the short term, aiding concentration, though it is less clear whether this is an improvement on never having taken caffeine.
There seem to be a lot of scientific literature around this question. If you agree that higher productivity at work should be a consequence of higher concentration, we have a lot of evidences.
The paper provides us with an extensive literature review of the past researches done on the effects of caffeine. It shows that many studies has demonstrated that regular coffee consumers show better performance at work. Caffeine seems to stop the decrease of performance as time past at work. However, that is only true for moderate consumption of caffeine. When people drink a large amount, the exact opposite happens, lost of concentration and lower productivity.
As a side note, I also came across this paper about the effect of Red Bull (which compare to coffee):