Maybe not if deregulation is across the board:
Were we to unilaterally liberalize zoning, some builders would see new opportunities in Manhattan. But it seems far more likely gazillions of suburban folks would see the benefit to building a cheap extra unit in the yard and renting it.
In terms of raw potential, it seems quite likely there is more “zoning-prevented housing” in the suburbs or in fairly low-density areas than in already high-density ones. The result could easily be that uniform upzoning boosts metro-wide population, but also causes a shift of population out of the center, into the ‘burbs, where geography may prove less of a constraint. The fact that less-regulated places also seem to be less dense suggests that this outcome is at a minimum plausible. That is to say, if density is your goal, deregulation may be a very uncertain way to get there because, while there may well be demand for urban cores (maybe), land use rules are just one of many supply constraints. Geography, higher construction costs, large existing investments, and the dramatically lower costs to adding equivalent supply in the ‘burbs all combine to suggest blanket liberalization could cause the typical household to reside in a less dense neighborhood than they did under stricter regulation.