Hello, taking Honor only to farm barbarians is only very rarely a worthy idea. There are much better ways to obtain culture. The culture that you make by farming barbarians will never pay off for itself because the cost for new policies increases exponentially. More importantly, the army that you use in this way is very badly used, there are much better ways to use an army. Scouting or just attacking somebody for XP over 30 is better. The best way is to rush to complete CS quests telling you to kill barbarian camps, so that you get 50 influence. If you manage to free workers for the CS you get an extra 40 and this means you can have 90 influence early in the game. So, the strategy of farming barbarians for culture can't be recommended.
However...the culture that you make by farming barbarians:
- does count toward City State quests, potentially helping you win their Culture quest
- counts towards total Culture output, making you less likely to be affected by ideological pressure of other civs.
- can help you get a fast Warrior Code (Honor 2) in order to rush attack a nearby civ.
The best ways to try the strategy that you are thinking of is with Aztecs or with Celts, who engage in wars for yields anyway.