Yes, but that's not the whole story

From Minimum Wages and Homelessness by Seth J. Hill.  From the Abstract.

America's cities continue to struggle with homelessness. Here I offer a factor, the minimum wage, that adds to existing individual and structural explanations. If there are negative distributional consequences of minimum wages, they most likely harm the lowest-skill workers many of whom already face housing insecurity. To evaluate this argument, I study minimum wage changes in American cities and states 2006 to 2019. Using difference-in-differences methods for staggered treatments I find that minimum wage increases lead to increased point-in-time homeless population counts. Further analysis suggests disemployment and rental housing prices, but not migration, as mechanisms. Scholars and policymakers who aim to understand and combat homelessness should consider labor market opportunities. Distributional consequences of minimum wage laws also merit further inquiry.

I don't disagree with the overall thesis; it is what economic theory predicts.  As Thomas Sowell notes in Basic Economics: A Citizen's Guide to the Economy, 

Unfortunately, the real minimum wage is always zero, regardless of the laws, and that is the wage that many workers receive in the wake of the creation or escalation of a government-mandated minimum wage, because they lose their jobs or fail to find jobs when they enter the labor force. Making it illegal to pay less than a given amount does not make a worker’s productivity worth that amount—and, if it is not, that worker is unlikely to be employed.

It would not be a surprise that jurisdictions with strong minimum labor laws would likely have higher homelessness.  People with low labor skills and non-cognitive skills will be priced out of the labor market.  

However, are economic conditions strongly associated with homelessness?  My impression is that the answer is no.  Homelessness seems much more clearly associated with local jurisdiction policies related to policing and social services and public health, especially with regard to mental health and with regard to substance abuse.  

The challenge is that jurisdictions that are likely to pursue the kinds of policing and social policies which foster homelessness are also the jurisdictions likely pursue minimum wage policies.  

Consequently, looked at through the lens of minimum wage, and it appears that people are priced out of the labor market and into homelessness whereas it is likely more accurate to say that jurisdictions which pursue minimum wage legislation are also likely to pursue other policies which are as likely or more likely to foster homelessness as the minimum wage policy on its own.