Yes, water plays a big role for a ton of reasons. If you have a carbon filter on your water system, its probably ok. Many will say they brew with tap water and its all fine, and it may be. Try this, brew two batches, use your tap water for one batch, and bottled water for the other batch.
Chlorine will go away if you heat your water, but now with the chloramines in water they say it wont go away, so now I am just paranoid and wont risk making a batch taste funny.
A whole book could be wrote on water chemistry and how it affects beer, I just choose to use RO water and adding salts back or just use good old bottled water that taste and smells fine to me, then I dont have to worry about it.
Campden tablets remove chlorine I have proved this with test from where I work. But I don't add them, because I really have not proved to myself that the campden tablets dont affect the beer. I try to eliminate all the stuff that makes me paranoid.
The water where I live, does not taste good, and has a ton of chlorine in it, so I just choose to stay away from it. good Luck