Alcohol from carbing in the bottle

When the beer is carbed in the bottle from the priming sugar, does it only create CO2 or does it also impact the ABV. What is the difference between the yeast and sugar process during fermenation vs carbing?

Same process and alcohol is the by product. You're typically adding the sugar in water solution so the net is about zero.

Some quick (and probably not 100% accurate) math tells me that if you bottled 50 bottles and used 5 oz of priming sugar, you'll get approximately .29 of a point (.00029) extra gravity in each bottle. So, in a nutshell, it affects ABV, but not on any noticeable scale.

Carbing is achieved by containing the byproducts of fermentation. So, if you add too much sugar, it will continue to ferment in the bottle, exceed the pressure capacity of the bottle, and cause bottle bombs.

Chemically, yes
Real world with our testing methods, no

Its also not a method I'd try to increase AVB, no good can come of it.