hollie, the data is not super-clear and some of the conclusions have to be inferred.
In the early days, we know that if a baby has any formula in the first week, the mother is three times more likely to be fully ff by the age of three weeks compared to the babies who have not had formula at this time - this is from Infant Feeding survey, and of course it is not pure cause and effect. The babies who are having problems bf are likely to be the ones who have formula and it's these underlying bf problems which precipitate the switch to formula, rather than the use of formula itself. Hope I have explained it ok!
If we look at the data showing introduction of milks other than breastmilk (so 'partial breastfeeding'), we see this gradually increases with the age of the baby (unsurprising). The number of babies not breastfeeding at all also increases with the age of the baby. We can infer from that that partial breastfeeding is strongly associated with earlier full formula feeding.
What we don't have is data showing the sort of scenario you describe - occasional convenience of night time formula - because all formula use is lumped in together, in the data.
Experience shows that this scenario - alongside a confident mother, who understands about how breastfeeding works, and who knows that several hours between breastfeeds will reduce her supply and how to manage that if she observes the signs - actually should not mean she is switching to formula sooner than she wants to.
So I should probably refine my statement about 'the majority of mothers' to reflect a sort of sliding scale :) Early on, partial breastfeeding is not likely to succeed long term (ie the mother ends up switching to formula quite soon). The later you introduce formula, and the more 'careful' you are about its frequency and volume, the 'safer' breastfeeding can be :)