can you add unique constraint sql after table full of data code example

Example 1: set column as unique in sql server

ALTER TABLE Persons
ADD UNIQUE (ID);

Example 2: unique constraint mssql

USE AdventureWorks2012;  
GO  
CREATE TABLE Production.TransactionHistoryArchive4  
 (  
   TransactionID int NOT NULL,   
   CONSTRAINT AK_TransactionID UNIQUE(TransactionID)   
);   
GO