No, as far as I know there is no on-screen indication about the current state of your water, unless you try to tap the well/pond/etc. I've used an iPod and an Android phone to play the game and neither has had any way to determine the water level.
Since the May 9th update, tapping any source of water will briefly bring up a water count as the water is added to your total. There still doesn't seem to be any way to display this counter all the time, but at least they also bumped the max up to 30 water.
Tapping a source of water starts a 2-3 second animation to add 4 water to your count. You can do other things during this animation as well, so I tend to tap the well and do something else, (like water a crop) and then tap it again if I saw 4 drops pop up.