Gail Pink, the floor mess will start as soon as the drain starts being blocked by whatever dirt will collect underneath the grille. And even in the perfect state shown in the picture at least some water will splash. If the place is not cleaned virtually after every other user, it will look shabby very soon, with either water around the drain or the stains you get when soapy water dries on glossy surfaces.
How long before the floor drain is clogged by hairs, bits of paper towels and all the other crap you find in public restrooms? How thorough will the cleaning staff be? My bet is that this thing will look nifty for about three days, then it will be one of those 'looked like a good idea at the time' failures.