I would guess that it plays a role, just as there are many other things that play a role - gestation, willingness to feed, ability to feed, taking steps to ensure supply, getting enough sleep for supply etc. So I would say a contributing factor but not the sole factor and in most cases not the deal breaker. For example I think gestation age and being born before the ability to suck has been developed is much more likely to be the deal breaker than vaginal vs. CS.