Yes water is wet as it could not be dry because that isn't just possible. The molecules in water make an object wet which eternally makes water wet. Saying it has to be covered in water to be wet to counterclaim this would be idiotic. My counterclaim would be water is already covered water so it is in fact wet. Hope this helps.
But then again you could tell me that when you're underwater you're not wet as it only happens when you get out of the water. This would make water not capable of being wet, so really I think you should do your own research to figure your question out.