"The aim is for a sugar free, alcohol free probiotic drink"
Short answer: No *(if using natural whey, sugar, fermentation)
Natural Whey is usually about 5% sugar (lactose) while not fermentable it is stil a sugar metabolized by humans.
Sour whey has less but still contains some lactos. 100% sugar free whey can be sourced but is heavily processed, and may conflict with the ideal of a natural healthy drink.
(Lactase can be used to break lactose down into fermentable sugars)
Using whey as a base without processing will have sugar.
Coconut / Palm Sugar
The major component of coconut sugar is sucrose (70–79%), glucose, and fructose (3–9% each).
Basically just a blend of table sugar (sucrose). Corn sugar (dextrose/glucose) and Fruit sugar (fructose).
Sucrose is molecule is 1 glucose molecule and 1 fructose molecule bound. This bond is broken in fermentation and human digestion to produce fructose and glucose for direct absorption by yeast and human cells.
In short coconut / palm sugar is nothing special. Just slightly faster to ferment and digest because a portion of it is already in monosaccaride form. It is completely fermentable, (yeast is able to convert all of the sugars mass into alcohol and cO2.)
Rapadura is unprocessed cane sugar, not coconut sugar. Sucrose is the sugar type (see above). But because it is unproccessed it does contain mineral nutrients that aids fermentation. Calcium, magnesium, iron.
It is possible Just not easy. You can make a probiotic drink that's alcohol, sugar free. Most will use fermentation to refine nutrients and make the drink carbonated, the but then you have alcohol. Alcohol can be boiled off, but you lose carbonation and denature proteins. However with the right equipment alcohol can be boiled out without heat by applying vaccum, the drink can then be force carbonated with the result of a probiotic sugar and alcohol free carbonated drink.