Yes bottled water that has not been opened can be brought onto the plane but the bottle of water you do bring on the plane through airport security must be frozen solid and not be melting.
If the bottled water is not frozen when you bring it through airport security then it will not be allowed through airport security.
But if the bottled water is completely frozen and unopened when it goes through airport security then yes you can bring the unopened bottle of frozen water through airport security and bring it on the airplane in your carry on luggage.
I bring unopened bottles of frozen water on the plane and I've never had a problem getting it through airport security.