Yeah we ask for one bottle at night (for our nightly water and to fill up one of the kids water bottles) and one in the morning, we don't use the ones they leave out in the lounge. Why would you feel strange asking for a bottle of water to take back with you? I see it no different than asking for a beer or two which they also offer in the lounge.
I was chatting with the lounge staff this past visit and we were actually talking about this exact subject. They said it was perfectly fine for people to request water, beers, etc. The only thing they enforce is the 2 alcoholic drink per person at one time policy (but you can come back in a few minutes for 2 more, just can't walk away with more than 2 at one time). They also don't like when people take the entire bottle of wine with them to the tables in the lounge or to their rooms (and this does happen!

), it's ok to pour 2 glasses worth and that's all that's in the bottle so be it, but don't take off with the bottle.