It's definitely a fair theory if you look at it hypothetically, but I think it sort of fails to acknowledge the effect on microeconomic behavior such a policy would create. It's basically just the age old debate of whether to help someone, or allow them to help themselves.
For the most part, this just sounds like an extension of the basic welfare system. Welfare legislation was made by FDR primarily because vital members of the labor force and economy (general public) were so deeply impoverished that they really had no option or capacity to pursue a macro-economically beneficial profession. By creating a government that provided the basic necessities, the once impoverished public could now invest in more "capital" rather than "labor." If people aren't focused on whether or not they will be able to eat at night, they will then be more inclined to follow more long term pursuits, that are exponentially more beneficial in the personal and national sense, but that require more sacrifice in the present. Education is an example of one of these pursuits.
The biggest issue in my opinion of welfare is that once the intentions it set out to meet were more or less met, the system remained in place and became feeding ground for manipulation of the system and bureaucracy which together also hurt efficiency of government and society. Generally, when there is no safeguard in place such as welfare or whatever, people have more incentive and consequently more motivation to dig themselves out of their hole. It's definitely true that having a debt free life made by hard earnings is still more desirable than a life dependent on welfare, but with people on that brink of motivation (that is to say they could very easily become a life-long hobo or just as easily create a self-sustaining lifestyle), knowing that safety net is there certainly has some effect on motivation and human choice.
So the question becomes what is the cross-proportionality of an increase in spending and the increase of people classified as these "life-long homeless" it would cause. I also think, as a general rule of policy, that more regulation, programs, policies, etc. tend to create more inefficiency just because of the bureaucracy that has to be dealt with and the increased opportunity costs. Policies are only successful economically if that decrease in inefficiency in one area is less than the gain in efficiency another area may see through the policy change. (i.e. hospitals may become more efficient in not having to deal with the recurring medical issues of homeless).
To me that's the biggest argument to consider, and I can't say which is right because it is based purely on speculation and estimates. The best advice we can get is from previous, similar policies/programs and what there negative, positive, and unintended consequences were.
I also have been studying for a test for hours now too so my brain is pretty shot. I could be talking completely out of my ass right now so feel free to rip me apart. These were just my initial thoughts.
