I highly doubt there's an exchange that support withdrawal to bech32 addresses, but not legacy addresses.
when you send funds to P2PKH based address which starts with 1, it automatically selects it while you chose segwit network.
There is no such thing as segwit network. We have only one bitcoin network.
If binance or any other exchanges say so, they are using wrong terms. We have segwit address, not segwit network.
but just to be more sure in order to avoid losing funds, reach out to the support of the exchange you are referring to or try out with a small amount that you don't care to lose.
As mentioned by OmegaStarScream above your post, in the unlikely event an exchange doesn't support withdrawal to legacy addresses, it should give you an error.