I've found the opposite to be true in every version of FFH2.
Whenever I see a promoted barb unit, it seems to be damaged. I asked in one thread if barb units were unable to heal. The AI seems to usually make them move and/or attack rather than stop to heal. I noted that even wounded units that ended up guarding a den or a goodie hut NEVER healed.
I think as you get into the higher difficulty games, though, the barbs get promotions and then do show up with full health.