Rather nice rifle there Hoot, fantastic work done on the inletting for that peep!
I can only say having a BRNO ZKK with its own pop up peep that it could be used in whatever combination sighting/load that you the owner requires.
If you want to use it with both front & rear sight because your eyes aren't the best due to aging then do so if it works for you mate!
Normally front & peep, the rear should fold.
What is your rifle, never seen a peep like that before, if you have a few more photos of your rifle can you show us please?