No.
If you want to resupply a field, you have to land/drop "Airfield Supplies", regardless if Airfield, Vehicle Field or Port.
You can either drop them like troops. Or you land, open door, and drop them on runway.
Each supply run cuts downtime by 15mins, so dont expect barracks or radar to pop up just because you did one singe resupply run. It takes several runs or even better the combined effort of several people to bring a field fully back up.
"Vehicle Supplies" are not for Vehicle Fields as you might think, but to resupply individual ground vehicles in the field.