Speaking from experience here. They have enough time. Most of them are completely politically uninvolved, but the ones who do know about politics are very frequently conservative, so i'm not entirely sure how to go about this.
It would make a lot of sense for rightwingers to mobilize the homeless and it probably won't be as difficult considering homeless people get a huge amount of aid from churches.
I think there's potential there, but it's hard to ask people that can barely sustain their existence to spend time they could be using to earn money is a bit complicated, if there were some true promise of true economical compensation, maybe, but for that you need to expropriate some land which would never happen in the US because their military industry is too big, that generally happens like in countries with heavy levels of peasantry.
This happened vaguely during blm with a police station. Mobilize the homeless and convince them they can stay in a police station, which would benefit somehow or something... not sure.
A handful of homeless/very poor come out during protests already about housing rights or to increase welfare. At least 1 homeless guy i met goes out to every antimask protest. A lot of them go out to church services on sunday, even the church services that are not in a shelter.
Or if a riot has like the promise of seizing a target again, that's something. But i wouldnt recommend a riot.
What about trying to promote some anti work shit on /r/homeless plus trying to create groups of like minded people who are in the same situation? It may be a better way to try to start something than in person.