Nope. Allocating space for cars and prohibiting the orgy of real estate densification improves the homelessness situation. It puts less stress on people to move into The Downtown, so they are more likely to stay in more reasonably-priced areas.
The argument that density puts stress on people to move _towards_ that density seems to me to have the direction of causation reversed. People look at prices when they move, not density.
Allocating space for car parking does not help address homelessness. In fact, it hurts it a lot.