Most shows have a specific time that the doe has to be milked out by (usually 12 hours prior to the show give or take) to show in the conformation type classes. Like Stacykins said, if the doe is a heavy producer and if the show is running late or she spent a lot of time in the show ring, yes she's going to be full. Ideally you want the does udder to be full but not engorged. A full udder gives a nice rear udder height, which of course is great for competition. If the doe is so full she is dripping milk, and you decide to milk just a little out to take the pressure off, the first place that milk comes out of is the top of the udder. So... it's kind of a tricky thing getting that balance of full enough but not too full. That being said, all the 4-h shows I've ever seen for the showmanship portion of the show requires the doe to be completely milked out as it's not about the doe's conformation, but about how she is handled.
My suggestion would be to contact your local extension agency (if you are in yuma county, they have a website, I just googled it). They will be able to give you the rules for 4-h shows.