Not at all. The plan is to ban private vehicles and through traffic within the cross town streets (East-West direction, numbered roads) in Manhattan.

Larger cross-town streets like 14th, 23rd and 42nd would remain open to all traffic. The smaller streets is where the ban would go into a place making them a single grade mixing zone for pedestrians, cyclists and vehicles. Service vehicles (delivery, garbage, taxis) can access these smaller streets but at a <10MPH speed.

Chicago at one time had an underground tunnel system for transporting goods, but it fell into disrepair, and is too small for moving modern trucks/freight. I think most/all of it is closed off today; although the city still uses some of it.

Singapore's Certificate of Entitlement (COE) system works really well to reduce cars in the city (you have to bid on the license to buy a car, which can run S$30k to S$90k depending on the type of vehicle, time of year you try to bid, etc. .. and that doesn't include registration or the actual cost of the car). But that's a situation where the city is small and .. literally its own country. So it obviously wouldn't work in NYC or anywhere in America.