We rang at around 9pm. Quiet as a mouse
If you're wanting Cinderella's Royal Table though, you absolutely MUST dial a minute before the lines open, and keep hitting redial until you get through (180+10 days before). Otherwise you'd be very unlikely to get a table.
Having said that though, we made reservations about 28 days in advance this trip and got all the tables and times we wanted (and it's during free dining). So it's really not as hard as people make out!