ring unless it is slammed hard

Yes, potentially. A single incidence of noise exposure could damage your hearing if the sound was sufficiently intense. This is sometimes described as acoustic trauma

 (or, more specifically, acute acoustic trauma), as opposed to noise-induced hearing loss, which generally requires repeated or prolonged exposure to noise.

Just think you’re in a car and you have hit a truck head on and you don’t have your seat belt on. Face first into your windshield. What do you think you’re going to hit first? Your nose, jaw, teeth, cheeks, face, then maybe your chest. It happened to my Sister & her Boyfriend. 

I doubt it yet it's not impossible. I'm not able to imagine a door being shut with such force that the sound wave temporarily shocks the ear mechanism transporting the sound. Shotgun blasts are known to cause temporary hearing loss. Continued shotgun blasts will certainly cause a permanent loss.

It is exceptionally unlikely that permanent hearing damage could occur from a door being slammed. I do assume we're talking about a basic office hollow core door.

One way you'll be able to tell if you're approaching the threshold of hearing damage after a door has been slammed?

One night my girlfriend and I got in a very heated argument. It ended with her storming out of my apartment. I heard her car door open and then SLAM shut followed by a thud. She drove off anyway. We made up and apologized the next day and I walked her to her car.