I am sorry to say that the answer, in my experience, is not quite. The cork will be removed from the bottle, but not removed from the wine opener. Just use the pliers to twist out enough to remove. Simple.
I just tried to open a bottle with a rubber cork for the first time since I've owned it(bought it beginning of 2013), and it took a few times but eventually I got the cork high enough to just pull it out. The opener would not pull it out all the way.