Turns out, I did some research and found he could use the local Post Office as his mailing address for the ID. He went into the PO and the people there didn't want to deal with him. The basically threw him out (this PO has a guard, which is a little odd to me). I offered to go with him to the PO and sort it out, but he was unwilling, even after I made the offer multiple times.
But, the good news is that he ended up walking to the DMV (3+ miles from where I would see him) and he did get his ID. That's why he was able to get into that temporary home last year. It was a huge hurdle for him to get that ID. I can only imagine that anything that requires a lot more effort than that would be beyond his abilities.
I will say, too, that what drew me to him was that he seemed to never ask for money from anyone, but he was often present on the same block when I would walk to/from work. I started up a conversation with him and over time we became friendly, and I would buy him food when he said he needed it. It was clear there were other people helping him (much more than I was), so he often didn't have immediate needs for food. Shelter, though, that's the big issue and when I did Google searches for local shelters it was really hard to find anything I could take to him.