Why is adding a NOT NULL column with a default constraint instantaneous?
Yes, adding a column with NOT NULL and a default doesn't actually write the values to all the rows at the time of the alter, so it is no longer a size-of-data operation. When you select from the table, the columns are actually materialized from sys.system_internals_partition_columns, which prevents all the values from having to be written (until they are changed). Note that this doesn't work for all data types and requires Enterprise Edition.

Remus Rusanu explains this in more detail here:


Online non-NULL with values column add in SQL Server 2012 


Also, for an ALTER at least, we still can't show you a plan because SQL Server doesn't produce one, but to see I/O, you can use SQL Sentry Plan Explorer.* This screen shot shows adding a column, c5, "online" as described above, and then another column, c6, "offline" because LOB types are not supported. You can see the I/O is mostly expressed as reads rather than writes, but what's more telling is the (invalid!) UPDATE associated with the offline alter.


  


If you don't have Enterprise Edition, both statements will have the secondary UPDATE attached (and the associated reads). (And if you use the free version of Plan Explorer, which doesn't get the full query call stack, you won't see the above - you will just see an empty statement tree. A paid version is required to see the full query call stack.)

Note that SQL Server will produce an estimated plan, but it's not very useful. At all. And the estimated plan for an online alter is identical to the estimated plan for an offline alter.


  


*Disclaimer: I work for SQL Sentry.