Is it safe to apply a voltage to a cup of water, and then use the water in that cup as a voltage source for other electronics?
I suspect it wouldn't work very well. Water itself is not conductive, it's the dissolved ions in it that conduct. So it has a fairly high resistance which gets higher if it's purified. I doubt there would be enough current flow to drive a display.

Another issue with powering things through water is that running current through a solution is the basic mechanism of electroplating. The more current flows the more one of the electrodes will erode, and the other may oxidise. Can be minimised with gold-plated electrodes (e.g. PCB ENIG finish).