Outside of rent controlled units, the landlords determine the rent. And that means that the non-American 'nouveau riche' will benefit from the new units. The fundamental problem with Manhattan these days is that it has become an open air shopping mall and the tourists are no longer scared of us New Yorkers ... ;)
the problem with rent control is that it encourages slumlording. unless it's temporary and combined with construction projects it's a losing strategy. the rich benefit from everything. if the number of new units is small enough, then yes, the poor will see no benefit. but rent is pretty much a matter of supply and demand crossed with unit quality, and you're never going to decrease demand in a city center, but you can build low-cost units.
Not really expressing an opinion on rent control, merely observing. If increased density is coupled with a law putting a cap on sale to non-residents then there would be an incentive to build low-cost (heck, reasonable cost) units. Otherwise, it makes far more sense to build for people with silly money.