It might be correlated, and it might making a difference at the margins (eg the people who have a job and can afford to live in a car). But the vast majority of the homeless population does not fit in that margin. Most of them do have other problems preventing them from getting any job, like severe mental health, substance abuse, or criminal records. Affordability is a moot point when employment is unattainable.
Your link didn't address the other factors preventing a job, such as criminal records. Sure, severe mental health issues are only a quarter. And substance use is something like 40%, but significant overlap. Add in felony convictions and see were we land.
