To add the column with a default and then delete the default, you can name the default:
ALTER TABLE tbl ADD col INTEGER NOT NULL CONSTRAINT tbl_temp_default DEFAULT 1
ALTER TABLE tbl drop constraint tbl_temp_default
This filled in the value 1, but leaves the table without a default. Using SQL Server 2008, I ran this and your code, of alter update alter and did not see any noticeable difference on a table of 100,000 small rows. SSMS would not show me the query plans for the alter table statements, so I was not able to compare the resources used between the two methods.