SQL Server doesn't depend on domain membership, but it can use it for several purposes, so the only answer is "it depends".
As suggested, you should be careful about authentication: if database access is granted to domain users/groups, it would not work anymore after a domain change (unless domains are trusting each other and some other measures are in place); if you're using local Windows users/groups on the server or SQL Server's internal authentication, the you'll have no problem at all.
Another thing to be careful about are SQL Server's service accounts, i.e. the accounts that are used to run SQL Server itself; if they are domain accounts, SQL Server services will not be able to start anymore after the domain change.