No.

Unless you redefine community to mean 'anyone within a particular geographic area' which renders the concept meaningless.

I get that they are not necessarily a part of their community, but the responses to my comment have been that he is necessarily not a part of that person's community just because one is homeless. What about the area in between? Like couldn't a person befriend a "random homeless person", and then that person becomes very much a part of their community?

they're part of the homeless community, but that doesn't help much. Homeless people do try to look out for each other, but lack of resources and personal demons make that hard. Community is far more than physical proximty; it's often the opposite where living near each other is a symptom of the underlying values, beliefs and shared traits. There are lots of communities in the same physical area.