Moorhen, you aren't going to get the sort of precision you ask in your final sentence, sorry. No one would be able to do a detailed study at that level.
It would be impossible to measure.
What we do know is that exclusive breastfeeding supports the normal, physiological growth and nutritional status of babies better than anything else, and that this is 'dose related' ie the less breastfeeding you do, the more this support is compromised. This means that one bottle a day after 14 weeks is a lesser compromise than 2 bottles a day after 6 weeks, but not as much as half a bottle a day after 20 weeks!
In real terms, unless you have a very allergic or sensitive baby, one bottle a day after 14 weeks (ie established breastfeeding, which is likely to continue very well with just a single bottle a day) will make no measurable difference to his health.
But what you feel about it is also important to your emotional state and your confidence. If giving a bottle will make you feel bad, or embarrassed to tell people, or unhappy, then the (possible) benefit of more sleep is lessened. If the (possible) benefit of more sleep is a wonderful and tempting prospect that allows you to feel more lively, enthusatic and energetic, then this might counter any (possible) effect on your baby's health.
In the end, it's a personal choice to do with feelings rather than stats on health effects.
Not much help, probably, sorry