You just won't be able to add a UNIQUE constraint on a COLUMN with duplicates datas.
In SSMS, the error message is something like that
The CREATE UNIQUE INDEX statement terminated because a duplicate key was found for the object name 'dbo.<Table>' and the index name '<constraintname>'. The duplicate key value is (<NULL>).
Could not create constraint. See previous errors.
So you can be quiet, you won't lose any data.