When taking damage to an outfit, does damaging an arming space also apply a -1 to the outfit's die?
They stack.

Damage Markers can be placed on any Section of an Outfit 

An outfit is made up of sections of two types; use spaces and empty spaces for storing cargo i.e. A use space is considered to be a section of an outfit. Therefore this rule

Damage Markers on an Outfit cause that Outfit to become less effective. Each (damage  marker) placed on an Outfit reduces rolls by 1 

means that damage anywhere on an outfit will cause it to be less effective.