No, the cork compound is on the inside. The sole is a flex-leather sole. If I'm not mistaken, the flex soles are what are called "waterlock", meaning they're treated with oil so are more water-resistant than other leather soles. But they're still leather, and that's what will touch the ground.
Sorry, I have to jump in and provide a slight clarification. Alden has their standard single and double leather soles which are oak tanned. They also have the oil soaked soles which provide superior wet weather performance. I have heard that they are a pidge softer than the standard oak tanned soles. The single oil soaked sole is known as the "flex sole" or typically called the "flex welt". The double oil soaked sole is known as the "double Waterlock" sole.
Other than that slight clarification, my friend speaks the truth. Alden applies a small layer of cork for comfort under the insole prior to attaching the outsole. And the oil soaked soles are still made of leather and if you like Toppy's, this may or may not cause you to rethink that practice.