I would say a big emphatic NO.
Adding sugar cancels out any health benefits carrot juice offers.
Sugar DESTROYS the immune system.
Here is my basic daily juice, 3 or 4 med-lrg carrots, a wedge of lime, 1/2 to a whole apple preferably granny smith (less fruit sugar) and a thumb size piece of ginger (start out small on ginger and work your way up as it has a bite going down)
I add to that a handful of spinach or parsley, a chunk of pineapple, and maybe 1 strawberry