Well, with this new script, it takes care of everything:
DECLARE @dropIndexSql nvarchar(4000)
SET @dropIndexSql = N'DROP INDEX [Advertis].[AddUser]'
BEGIN TRY
PRINT @dropIndexSql
EXEC sp_executesql @dropIndexSql
END TRY
BEGIN CATCH
Print ERROR_MESSAGE()
END CATCH
IF NOT EXISTS (SELECT * FROM INFORMATION_SCHEMA.COLUMNS WHERE TABLE_NAME = 'Advertis' AND COLUMN_NAME = 'AddUser')
BEGIN
BEGIN TRY
PRINT @dropIndexSql
SET @dropIndexSql = N'ALTER TABLE [Advertis] ADD [AddUser] int'
EXEC sp_executesql @dropIndexSql
END TRY
BEGIN CATCH
Print ERROR_MESSAGE()
END CATCH
END
ELSE
BEGIN
BEGIN TRY
SET @dropIndexSql = N'ALTER TABLE [Advertis] ADD [AddUser-Temporary] int'
PRINT @dropIndexSql
EXEC sp_executesql @dropIndexSql
SET @dropIndexSql = N'UPDATE [Advertis] SET [AddUser-Temporary]=AddUser'
PRINT @dropIndexSql
EXEC sp_executesql @dropIndexSql
SET @dropIndexSql = N'ALTER TABLE [Advertis] DROP COLUMN [AddUser]'
PRINT @dropIndexSql
EXEC sp_executesql @dropIndexSql
PRINT 'Renaming the field'
EXEC sp_RENAME 'Advertis.AddUser-Temporary', 'AddUser' , 'COLUMN'
END TRY
BEGIN CATCH
Print ERROR_MESSAGE()
END CATCH
END