It's never stopped me.OOPS! I guess I should read all the responses before I add my 2 cents.
Those ramped water bowls are great for lizards and snakes, but they are a terrible flipping/drowning hazard for tortoises. You should remove it ASAP. More than one member here has come home to find their tortoise flipped over in one of those. Terra cotta plant saucers sunk into the substrate are much better.Tank acquired a new liking of sleeping under his water bowl.
It does get dirtier, but it won't kill your tortoise. Fair trade off from my point of view.They live out doors where rocks are all over the place. I would think a saucer would get dirty more easily and things would get in it. My turtle loves to climb and loves his water dish. I could add the saucer for a few days and see how he responds to the saucer but he likes everything in his enclosure.