Yes, breathing apparatus shall be considered as an assembly in the sense of the PED, the items of which have to be conformity assessed according to their individual design pressure and other characteristics, and the assembly shall be subjected to a global conformity assessment.
Reason:
Breathing apparatus is personal protective equipment and, as such, covered by the PPE Regulation (EU) No 2016/425. This does however not exclude it from the scope of the PED dealing with the associated pressure risk.
See also PED Guidelines A-10, B-16.
Note:
The same reasoning applies for diving breathing apparatus.