Well if we look closer at the information it looks like no for DoW/M
Disciples of War and Magic
Completing level 45 caravan escort duty will benefit the corresponding hamlet’s supply rating.

But yes for crafter and gatherers:
Disciples of the Land and Hand
Delivering items requested by the hamlet militia quartermaster, or any materia-enhanced weapon or piece of gear, will not only contribute to the hamlet’s supply rating, but will also earn you an anima boost based on the type of item donated.
-Materia enhanced gear(no lv indicated), and then of course whatever items they are requesting.