If it's a 'sport' [spontaneous mutation], the other chickens are fine. If it's recessive white, then yes, both parents have white in them and there 's the chance the siblings could be carrying white also.
If the [opposite sex] siblings of the white chick have some good traits you want to keep, you can test cross them to the white chick. IF the sibling is also carrying white, some of the chicks will be white. If there are NO white chicks from the cross, the sibling isn't likley carrying white and would be safe to mix with your new line.
If i were closer, i'd volunteer to buy some of your test chicks since i'm not looking to improve a breed but like dark brown eggs.
Good luck