If you cauterize in the first thousand turns or so then you will get a second shot at cauterization before proceeding into infection territory where it can't do anything, which since cauterization is a 50/50 shot means you have a 75% chance of being healed (or at least put into recovery).
For comparison:
Chance of healing naturally while bitten: ~30% (This is further increased by 10% [vitamin shot is around +10% IIRC] and is reduced if you are currently recovering)
Chance of healing if cauterized twice fairly immediately: 75%
Chance of healing if cauterized once later: ~50%
Chance of spontaneously recovering from infection: ~20% (modified same as bite recovery)
Total chance of natural recovery: ~50%
It still helps, but it's a bit of a gamble because things can go much worse for you if you get unlucky and fail to remove the bite wound. Also since recovery is a much more arduous process now it's a bit of a gamble on that. Even a single cauterize failure can provide a fairly large increase in recovery time (all during which you are more susceptible to further bites/infections). Generally you will want to use disinfectant or first aid kits if you have them, since they don't cause an increase even if they fail (which should only be 5% and 1% respectively). For a single infected wound you might want to use a first aid kit (which now cure bleeding, biting, and infection as well as giving a slight painkiller effect on top of that) as it will work fairly well, but for multiple infections you should use antibiotics, since it treats them all simultaneously and grants decreased recovery times.