Do unconcious people who fall in water die?

I have successfully performed a non-lethal take down, but the body fell into the water. If I am going for one of the no kills achievements, do I need to worry about them drowning?

Yes, if an unconscious body falls into water, it counts as a death, and the blood is on your hands.

If you go back down to collect the body, you should see the dead symbol rather than the sleep symbol. If you're on the bridge level or one of the other places where this is impractical, you may want to reload from a previous save just to be safe.

See here for a comprehensive list by galacticninja of everything that counts as a kill against you: https://gaming.stackexchange.com/a/90107/5398