Yes, you can alter your column from being varchar(1000) to be nvarchar(MAX) without data loss. Beware, though, that this is a size-of-data operation, so it can take some time if the table is big.
You could also keep it as varchar but change the collation a UTF8 collation. Or may be you already have a UTF8 collation, since you talk about 1-to-1 character byte ratio? If that is the case, there is no reason to change collation or data type, since you already have full Unicode support. But you may want to increase the max length or make it varchar(MAX) in that case.