The tax is reasonably small enough that I wouldn't expect a lot of wealthy people from divesting from their properties, but it's probably going to make them think twice about buying new properties.
That second-order effect is the important balancing act for any locality-based wealth tax. If you make the tax too high it starts discouraging the behavior you're taxing, which can paradoxically reduce overall tax revenue.
France discovered this the hard way when they implemented their first wealth tax: Many ultra-wealthy people moved their capital out of France to avoid the tax, which was suspected to have had an overall decreasing effect on tax revenue from that demographic. They replaced the wealth tax with a property tax, which probably played a large role in inspiring this pied-à-terre policy.