Sure, but note that there isn't a single mention of the word "homelessness", or even "homeless" in that report.
But here's the thing: homelessness is to do with owning/renting a house. And the reports I gave focus on the issue of homelessness rather than just poverty in general. Income inequality makes home ownership/renting less affordable for those at the bottom than would otherwise be, not because of their higher earnings but because house and rental prices are higher because of the inequality.
So if income was more equal, house X might cost 500 a month and person A might have been able to afford it. But because of income inequality, and more people able to afford higher prices, the cost of X is, say, 700 a month. Or more. This then puts that rent outside of person A's ability. Sure, they can find a cheaper place... and that's ture... up until the point they can't, because this same dynamic happens all the way up and down the chain.
One solution is to lift everyone's buying power, sure, but if the inequality remains then this will inevitably inflate housing costs and you're left with the same issue.
Build more housing is another solution, with the increased supply deflating the costs of rents/ownership. But then unless this is a permanent solution - i.e. a constant new supply of sufficient housing year after year after year, you'll eventually end up in the same position. And the fact remains throughout that period that inequality still impacts the cost of housing to the detriment of those at the bottom - only now they wouldn't be homeless.
Yes, this is a simplistic rendering of an argument, but it seems clear that inequality does have
something to do with homelessness.
Here's another link: