Yes, the the formal photos were taken for both public and private use. NAOTMAA often signed and sent them to family members -- some formal photos from the collection of Irene of Prussia appear in The Jewel Album of Nicholas II. Others were framed and displayed in their private rooms. Alix had dozens in her Mauve Room, and Nicholas's desk was also littered with them. OTMA even took some into exile and pinned them to their bedroom wall in Tobolsk. If you look carefully, you can see formal photos on the walls and shelves in vintage photographs of the Alexander Palace.
I'm sure the photos were also used for publicity worldwide -- in newspapers, announcements, commemerative booklets, etc.