I have the exact protector that the OP linked. I haven't fallen on it but it is so thin that I wouldn't want to - I only ever wore it 2 or 3 times. If you're looking for something that will prevent tailbone injury, waxel pads are the way to go. I have fallen on mine and have been left unbruised so far... They're so popular among skaters, that it doesn't look strange on the ice and they're not very noticeable if you're wearing tight black leggings to hold it in place. If you are self conscious but want to go the waxel pad route, wear a long top that covers most of it. Like hanca said, you may have to choose between aesthetics and comfort.
Another idea is a skatingsafe pad. I'm not sure what the tailbone pad is like. It's an interesting shape, so I just went for a waxel pad. But I have skatingsafe knee pads and they absorb shock almost completely. They are very thin, so you wouldn't even notice them unless you really looked for them. That might be worth looking into.
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