I think all the non-combat skills should.
Doctor gives you a living anatomy-esque perk by default.
Repair gives your armour bonus damage resistance.
Outdoorsman gives you a HP bonus.
Speech gives your mercs a bunch of combat bonuses.
I have thought through none of these, they're just random examples. Obviously the 'skill perks' have a greater effect the higher the skill.
Repair gives armor-fixing, so relative armor levels already give a net bonus to repairers.
Outdoorsman could increase healing rate very slightly as well as AP regen very slightly due to the physical conditioning that comes from being an outdoorsman.
Living Anatomy already presumes that knowing where to hit in a surgical sense translates to the agility and skill necessary to make some kind of mystical targeted shot.
Makes sense in "game terms", but not realistically.
Speech could make mercs less buggy (fix the merc bugs, but implement the fix as a gradient influenced by speech).
Giving them combat bonuses wouldn't make much sense unless the merc commander had some special skill or insight to share with the mercs, in which case Speech would help with the transfer of that information.