Can falling onto your tailbone cause paralysis or be dangerous, and if so how likely is it?

It does not. The nerves that supply your body exit the spinal column before they get to the tailbone. The usual injury, separating the tailbone from its attachment/cracking or breaking it has little long term effect beyond discomfort.

Am unaware of any cases of paralysis caused by trauma solely to the coccyx (tailbone), but certainly can result in intense pain, especially when fractured. Will be almost impossible to sit normally, and a donut cushion will be required until healing completed. This is called coccidynia.