Can tap water be used to top up the water level in a battery if the plates are exposed?

If you have a maintenance-free battery you won’t need to top it up with water. In batteries where you can top it up if needed, you should use distilled, deionised or demineralised water. Tap water can produce mineral build up that blocks the pores and coats the plates of the battery. 

It’s unwise to let the water level drop to leave the cell plates exposed as they can dry out and lead to battery failure.  Battery warranties won’t cover a serviceable battery that has failed due to water loss.