Yesterday I transplanted 6 plants from Dixie cups into my DWC hydro system. I tore the paper off the plug of dirt and then rinsed the roots clean under cool running water. I transplanted them immediately into the hydroton one by one. They're doing great now. They didn't even wilt.
My plants were only 9 days old and about 3.5 inches tall, though. The roots weren't all that big yet so I'm not sure if that will be a problem for you.