You don't get tickets for any of the food and wine events, just a confirmation number. You check in with a cast member at the event, who has a list of registered guests. You get your wristband and the souvenir wine glass and notched "holding plate", along with a color-coded event booklet of the food and wine stations in the venue.
No matter if you book it over the phone a month in advance, or book at Guest Relations a few days in advance, it will be prepaid in full. Because the World Showplace venue holds a lot of people, I don't find I need to book it on the first day the event bookings open.
I intend to book my other event on the first day, and book Party for the Senses in mid-September, so it will hit my next credit card statement. It's a month before my trip, and I don't think it would be sold out.
But, that's a lot of info you probably didn't need.
I don't know if it does sell out, but I wouldn't wait until a day before to book it. I'd suggest booking it at least 2 weeks out through the Disney Dining phone number.