No it isn't. Civilization-level benefits, like receiving science when you spread your religion with Council of Elders, or receiving faith/golden age points from conquering with Hero Worship, apply immediately after you found your religion. You don't need the majority of your cities to follow your founded religion. On the other hand, faith on kill from God of War is completely lost if conquering a city leads to the majority of your cities (or 50%) being faithless.
To be clear, I am not concerned about the conquered city not receiving the city-level benefits like +1 faith from barracks and whatnot. My issue is with the civilization-level benefits from God of War/Defense/Expansion being completely wiped out by conquering a city.