No, a tax will always reduce demand \saying otherwise basically ignores decades of established economics.

> that creates incentives for the city to cater to them

What does that even mean? If catering to the wealthy was profitable, everyone would do it. Just look at Dubai, it's built entirely around that model, and it's a brutally competitive space. NYC attracts the mega-wealthy for a different reason: network effects. Meta-wealthy come to be around other mega-wealthy people.