No. If you want to backsweeten & carbonate, you must either use a non-fermentable sweetener (stevia, nutrasweet, xylitol, etc...) to back sweeten & then add fermentable sugar to prime & carb. OR backsweeten with a fermentable sugar, prime & then allow the yeast to partially ferment it to carbonate, then pasteurize. If you have a kegging setup, you could also backsweeten & stabilize, then force carb. As for the amount of priming sugar (corn sugar/dextrose) to carb, the standard amount is (by weight) 4-5 oz. (113.39g - 141.74g.) per 5 US gallons of cider/beer; according to the online standard/metric calc. That does NOT include any amount for backsweetening.
You could both back sweeten & carb by adding either fresh juice or juice concentrate, but you'd need to pasteurize to avoid bottle bombs & do the math as to how much would be equal to the amount of sugar you'd need.
Regards, GF.
