I've spent lots of time on medical support lists. There is nothing worse than getting a bunch of cranky, miserable, doped to the gills sick people together who all want to demand that they be the person being accommodated because they are so fucking miserable, as if no one else's misery counts.
On some shitty, shitty forum I used to spend time, they liked to promote this concept of "comfort in, dump out" which posits that one person gets to play the victim card and everyone else must cater to their needs. It's a popular but totally broken mental model and it goes utterly kablooie when everyone in the group has a serious health issue.
In practice, you can't have useful, meaningful discussion about what works because everyone is walking on eggshells to avoid setting off the most incompetent and histrionic members who absolutely don't want to hear that if they did X, they might not be so sick because that's "blaming the victim."
Furthermore, there can be germ control issues with bringing your tech into a hospital setting. It introduces challenges to sterilizing everything while there and it can mean you carry hospital infections with you when you leave. Some wards will not allow you to bring in tech because it can interfere with their tech, like heart monitors.
People in the hospital having surgery or under quarantine for infections can be given a long list of restrictions for purposes of germ control while there.
Furthermore, the tech already exists. From Twitter to Facebook to email lists and more, there are plenty of online social spaces and I have done my share of virtual handholding for an internet friend stuck in the hospital with a direly ill child. You don't need a special space for this. In fact, a special space for this tends to be a worst case scenario. It's better to chat with your knitting buddies online or whatever than to impose on other sick people exclusively.
For hospitals, I'd be nervous about the legal implications of implementing such a platform - specifically HIPAA, since you'd be facilitating the communication.
I like the idea, as it could be useful for building communities for patients that could otherwise become isolated and non social (which can effect health outcomes).
No necessarily "dating" or "by interest" groups - but it could be a great idea for someone who just admitted to "learn secrets" and ask questions to someone who been there for 2 weeks or so.