I doubt they will. If we look at NY's Bitlicense, it can take crypto businesses years to actually obtain it, and that's just time time aspect of it. It also involves a lot of cost that very likely will scare off a lot of businesses because there doesn't seem to be enough user demand to justify that sort of an allocation of time and money.
Bitstamp was granted a Bitlicense this year after having applied for it in 2015! https://www.coindesk.com/bitstamp-granted-bitlicense-will-expand-crypto-services-in-us
Binance with all the garbage it has listed will face serious difficulties to be granted such a license, or they have to please the NYSDFS by excluding the more exotic stuff they have listed and only allow NY residents to trade Bitcoin, Ethereum, Litecoin, etc.