No, but people are mobile, and the houseless are also people who communicate through the internet and share where assistance is available.

If free, safe lodging is available without restrictions, demand will quickly outstrip supply with folks moving from other cities (LA, Seattle, Portland, etc) to fill the available rooms. It's a $50 bus ticket, city officials will likely fund these tickets for them to get to SF to take advantage of this. SF had programs for this exact thing to get homeless out of SF [1]

1 - https://www.vice.com/en/article/bvg7ba/instead-of-helping-ho...