That or trim some of the logistics admins. They provide the least real benefit to the unit and we have the most of them. We want to keep a couple of transport admins, but we could trim a few there as well.
I just deleted a bunch of admins to see what happens. Short version: you lose ALL the bonuses and cannot deploy on missions at all.
Evidently there is a "administrative man-hours" requirement, which is met by having a NUMBER of admins. The bonuses listed in the campaign guide were for having GOOD admins. It never occurred to me that people would just fire everyone but the minimum number of GOOD admins in order to keep the passive bonuses, so I didn't bother exploring what happens in this instance. Whenever I play, I just hire a full admin platoon (28) and be done with it.
You have 19 current admins. Each admin contributes 20 hours/week in administrative requirement hours. From the looks of things, each person in the unit generates roughly 1 hour of required admin hours. If you don't have enough admins to cover the hours, the whole unit basically locks up. Probably until you fire people, but I haven't tested that yet.
tl;dr, firing a bunch of admins is probably a bad idea.