Warfare and Staff is an odd combination. Yes, you can use a Staff with almost all Warfare abilities (sans those that require a Shield of course). BUT.
Staff works against Magic Armor, and Warfare abilities are resisted by Physical Armor. So you aren't able to break down Physical Armor with your weapon.
Also, the benefit of Warfare doesn't work with the Staff, since it only affects Physical Damage. A Staff that does Air damage gets extra damage from Aerothurge NOT Warfare (as an example).
So while you CAN use the Staff with Warfare its not a good idea unless you're taking the Warfare ability for some of the Buffs and not the Attacks.