Hi Mack,
Yes, I did this exact same thing when upgrading from 11.2.4 to 12.0.4 (and now 12.1.3) using SQL Server.
Just a heads up when you point Cognos 12 to the copied DB for the first time, it has to upgrade the database schema. If your database is huge, the initial startup will take a while. Don't worry if it looks like it's hanging just let it run.
As always, make sure you take a Database full backup and a servers snapshot before hitting the switch!
Thank you,
Abbas