The way I see it, the possibility is not so much about contracting a disease. More like displaying symptoms of the disease/medical issue that a connected astral body might have. For example, a couple weeks ago, me and one other person were in communication with a spirit that's been contacting me for a couple months about helping them. When "in the astral realm", during this communication, although I've invoked my protections and was wearing my talismans, we're still subjecting ourselves to an electromagnetic type of connection that can include a multitude of experiences like emotions, thoughts, memories, and even physical sensations that aren't ours. So during this consultation with this spirit, the question comes up about how they passed. Now, the way I handle these kinds of sessions are that when the question is asked, the mediums taking part don't communicate right away. We take notes and then share afterwards unless something comes up directly relevant to the next question. But in this case, me and the other person looked at each other after writing notes and both said "chest pain". It felt like a mini heart attack for both of us for a very brief period of time. It freaked me the fucked out initially until I snapped back and realize that the sensation was not "from" my body. But my body sure as hell responded to it.
So in a nutshell, I believe that the symptoms of someone else's disease are what one can experience. But if not protected and left unattended after prolonged exposure, I'm sure it can help manifest itself it an actual disease in our bodies.