I think that's not necessarily the most important question. A more important one is "are more homes (dwellings) the easiest way to reduce homelessness?", and "do more dwellings reduce the number of rough sleepers?", to which the answer is "yes". During Covid lockdowns, the UK housed all street-homeless people at four days notice (other countries did this too). This was possible because of the sudden availability of hundreds of thousands of vacant hotel rooms.

For at least a little while, a massive influx of supply of dwellings entirely eliminated rough sleeping in the UK, mitigating the harshest impacts of homelessness for thousands.

Yes. https://homelessnesshousingproblem.com/

When you examine an island of critical business development with desperate need for workforce yes, otherwise you will mostly find rent and prices that compromise life conditions. Basic needs aren't a market you can easily disrupt (unless you plan to let a class of slaves or poors be created).