No, it doesn't count. Sorry, chickies (and rooster?)!
Here's why: your body has to work to process this stuff...there's artificial flavoring and sweetener in it, not to mention the carbonation (which, by the way, makes you thirstier...). That isn't to say that this stuff is bad for you...it's not! It's certainly better for you than soda.

And it is tasty!

It just doesn't count as part of your water intake. When your body has to work to process the stuff you're drinking in order to get the water out, it doesn't have it available as fast as it needs to.
You need to drink at least 64 oz of clean, pure water. You can add ice, you can even add a slice of lemon or lime (and squeeze the juice into the water)--that can make it a bit more tasty, and the small amount of natural flavoring won't be hard to process like all the artificial stuff in the carbonated water.
Hope this helps! I think there's a thread around here that explains it better than I can--if I find it, I'll post a link here.