Definitely within the storage space by the definition given in 410.8 (A). Whats with that soffit though? Is it solid? Did the electrician during rough-in forget to set a box in the correct location? I bet that cover's a bit tricky to get off.
Who said an electrician did this? In addition to this, Dimmer on paddle fan, quad in bathroon has never worked, no gfcis on kichen counter, DW run from COLD water pipe, both sumps covered with carpet. Theres a handyman for you!
With the advent of LED lighting, as well as the sundry "closet organizers," I really think that it's time to consider the code allowing for suitably designed fixtures in close proximity to the clothes (or stored material)
I have seen at least two products that combines electricity and clothes rods. When we wire homes, we might want to consider placing a receptacle in the closet.