Actually yes...
- all Combat activities count during a Civil War/War period
Hence, technically you can win a War without ever entering a Conflict Zone.
However, standard Combat Missions are often scarse (depends on finding a Military Economy in the System) and the effects of handing in Bounty Vouchers for your Faction within the Conflict System is only about half as effective compared to Combat Bonds.
Still, the core issue remains - you'll need to support your Faction with Combat Activities/Missions or Bounty Vouchers or Combat Bonds, there's no way around that since all non-combat activities have no effect during the Conflict.