You must try and see yourself if it works with
convert option.
I don't think that regular trading is available for most unverified accounts in Binance, but I heard some people can still trade until December.
According to the
Binance announcement, those who are still not KYC verified won't be able to trade or use any products and services available from Binance.
So I think he won't be able to trade or convert any crypto from his wallet the only option for the non-KYC verified account is to withdraw.