Update: The rehab seems to be really helping. Leonard is far more alert and aware than he was when I last saw him (I work full time so at the moment that's once a week). He's been interested in messages sent to him, and more than that - he went straight for my laptop keyboard, and after a lot of effort and several false starts was able to give me his Facebook password. We went through some of his messages and saw some of his new feed.
Honestly, this is the first clear evidence I've seen that he's fully aware and has good memories of what happened before the crash. It's only in the last few days that any of us have seen that.
So, since my parents aren't the most tech-savvy people in the world, don't expect to see Leonard online often, and it takes a lot of effort to type even one word, so don't expect to get messages from him - but you might occasionally see him online!