Ok, so not much of an experiment; I'm pretty sure water isn't going to kill my baby. I'm not even convinced it's necessary, but some BLS mamas do it. I'm sure Buttercup is still drinking a lot, because she's still nursing the same as before.
I do give Buttercup water when I feel like she might have a bunch of food hanging out in her mouth or throat. Also, it's summer so sometimes I give it to her when she's hot. She never drinks more than an ounce at most, and I give it to her out of a regular small cup (the old school tupperware cups from the 70's). I figured, "why teach her to drink of out one kind of cup and then have to re-teach with another kind when when she gets older?" It also helps that my baby is a genius who doesn't need help with such menial tasks as drinking water. Naturally!
I started practicing drinking out of a cup with Buttercup after a bath. I figured, "Hey, she's naked and already wet!" I was surprised how little went down her front the first few times. She does have a tendency to try to lap it up like a little puppy, though.