im a tech at audi and have to say i'm miffed by the theory water leaking onto your brakes. how can water leak onto your brakes? everytime you go through a puddle a big puddle water gets splashed onto your brakes. at best they just won't bite for a corner if you go through a torrential, deep one that is...
as for pad sticking....the sliders get seized which is quite common, they will then bind. this infact happend on my own golf. it got to a stage where it was really bad and that will not give you any noise, but wear down you pads drastically and if you're on a motorway your disc will get very hot and go blue and warped being that under heavy braking at high speed you could experience brake judder through the steering but no noise.
so i am miffed tbh ....
sounds like a very expensive bill. road noise is usually a feathered tyre, being a budget one, vags have a lot of road noise or if its a humming noise it will very likely be a wheel bearing. simply jack you car up, spin the wheel and hold the spring, if you feel vibration through it, that wil tell you if its the bearing if you can't already hear it.