bklr, just to be clear. The process you described actually creates a new table, populates it, drops the old table and then renames the new one.
This is one way to create a new non-IDENTITY column but not necessarily the best way because it involves copying all the data and locking the entire table for the duration. That could be very expensive for large tables.
Also, bugs have been reported with the scripts produced by the design tool in Management Studio. I don't recommend that method for production systems. Better to create the script, test it and only then run the script on the target system.