Sekreterare does not change when plural? Is "The secretary" "Sekreteraren"?
Right, it's en sekreterare, sekreteraren and plural sekreterare, sekreterarna. All -are words work this way.
In addition, I believe all common gender -are words follow this pattern
In English, "does" would only be used here for emphasis if it were a rhetorical question. "All this paperwork we have to fill out seems to assume we each have several secretaries at our disposal - but who does have several secretaries?"
So it might be okay in that one special case, but in general it would be a poor translation, so it should not be accepted.