How do I demonstrate Transaction Log activity?
Pick a page containing a record in your table (use %%physloc%% to find one). 
Run DBCC PAGE before the DDL, write down last_lsn of the page. 
Run your DDL
Run again DBCC PAGE. Did last_lsn change?


If the last_lsn changed the DDL is a size-of-data updates-every-record kind of change. If the last_lsn did no change obviously the DDL did not update every record.

For a more elaborate way, you can track page write XEvents for a single statement (the DDL).