If you give a homeless person a home, then by definition, they are no longer homeless.
On a less pedantic note, yes, it should. Some countries (like mine) provide a secure place to live as step one, when helping the homeless. Having somewhere safe to sleep, keep your property, etc. makes all the other steps involved in solving your problems much easier, leading to a better success rate in getting people back on their feet.
I don't remember where I saw this the first time, but it did mention that this had become a thing in a few American cities too (this story was from Fredericton, Canada)
My city does something like this as part of our homeless program and we're at "net-zero" homeless. It doesn't work on it's own, but the tiny homes give people a stable place to keep their stuff safe and the elements off their bodies, it gives them an address they can use for things like mail and applications, and it gives social workers a place to find them reliably. It's the start of a long process to help them back to their feet.
I used to live in a town that did something very similar to this. It sorta worked but mostly did not. But as another commenter pointed out you need more than just homes. Obviously they help a ton but a lot of people need more help than just a roof over their head. Financially, medically, mentally, employment... It's a bigger, more complicated problem.
But it goes without saying that this is a step in the right direction and absolutely better than collectively shrugging our shoulders and walking away.